Claims:1. A method for acquisition of reflected or transmitted ultrasonic pulses and image reconstruction in an ultrasound imaging system comprising steps of:
acquiring the reflected or transmitted ultrasonic pulses using a transducer;
sampling the acquired pulses using an Analog to Digital Converter (ADC) at sub-Nyquist rate; and
reconstructing the image from the sampled reflected ultrasonic pulses, wherein the sampling and reconstruction is done by employing finite-rate-of-innovation (FRI) signal sampling and reconstruction.
2. The method of claim 1, wherein the transducer is a single element transducer.
3. The method of claim 1, wherein the transducer is an array of transducers with or without a transmit or receive beam forming.
4. The method of claim 1, wherein the ADC incorporates a sampling kernel selected from a group comprising non-periodic SoS kernel, sum of modulated raised cosine kernel, and sum of modulated spline kernel.
5. The method of claim 4, wherein point spread function or impulse response of the transducer is used directly for reconstruction of the image.
6. The method of claim 5, wherein the point spread function or the impulse response of the transducer is modelled by the kernel that has an analytic expression that is selected from a group comprising Gaussian, modulated Gaussian, or their truncated versions, polynomial splines.
7. The method of claim 1, wherein the reflected ultrasonic pulses are modelled as asymmetrical pulses using the fractional Hilbert transform or derivative based asymmetry modelling.
8. The method of claim 1, wherein the acquired pulses are convolved with the sampling kernel and the resulting function is sampled uniformly or non-uniformly in at least one channel in a multiplexed fashion, either in full rate or low rate.
9. The method of claim 1, wherein the method further comprises step of denoising to enhance signal to noise ratio, and wherein the step of denoising uses Cadzow denoising method.
10. The method of claim 9, wherein the denoising is done by sub-band shrinkage of undecimated wavelet transform using a generic risk estimator.
11. The method of claim 1, wherein the step of reconstructing the image from the sampled reflected ultrasonic pulses comprises the step of performing parametric reconstruction of time delays of the reflected ultrasonic pulses, and wherein the parametric reconstruction of the time delays is done by means of any or a combination of annihilating filter, matrix pencil method, method of estimation of signal parameters via rotational invariance technique.
12. The method of claim 1, wherein the step of reconstructing the image from the sampled reflected ultrasonic pulses further comprises the step of estimating amplitudes of the reflected ultrasonic pulses, and wherein the amplitudes are estimated using any or a combination of linear least-squares, weighted least-squares regression, iterative weighted least-squares regression, Huber loss function, and their variants.
13. The method of claim 1, wherein the step of reconstructing the image from the sampled reflected ultrasonic pulses further comprises the step of reconstructing each scan line (A-mode reconstruction) to result in a 2-D (B-mode) image and stacking to get a 3-D image.
14. The method of claim 1, wherein there constructed image possesses super-resolution.
15. The method of claim 1, wherein the method is used for medical imaging.
16. The method of claim 1, wherein the method is used for ultrasound or low or high-frequency acoustic wave-based non-destructive testing and evaluation of materials, equipment, or parts thereof.
17. A system for sampling reflected or transmitted ultrasonic pulses and image reconstruction, the system comprising:
a signal acquiring module configured to acquire reflected or transmitted ultrasonic pulses and sample them at sub-Nyquist rate; and,
a processing module configured to estimate time and amplitude parameters from the acquired samples of the reflected or transmitted ultrasonic pulses and reconstruct the image, wherein the sampling and reconstruction is done employing finite-rate-of-innovation (FRI) signal sampling and reconstruction.
18. The system of claim 17, wherein the signal acquiring module incorporates a sampling kernel selected from a group comprising non-periodic SoS kernel, sum of modulated raised cosine kernel, and sum of modulated spline kernel.
19. The system of claim 17, wherein the reflected ultrasonic pulses are modelled as asymmetrical pulses using Fractional Hilbert Transform.
20. The system of claim 17, wherein there constructed image possesses super-resolution.
, Description:TECHNICAL FIELD
[0001] The present disclosure generally relates to technical fields of non-destructive testing and medical imaging. More particularly, the present disclosure relates to a Low-Rate Super-Resolution Ultrasound Imaging System.

BACKGROUND
[0002] Background description includes information that may be useful in understanding the present invention. It is not an admission that any of the information provided herein is prior art or relevant to the presently claimed invention, or that any publication specifically or implicitly referenced is prior art.
[0003] Ultrasound imaging is a non-invasive imaging modality that is used to characterize the acoustic properties of a specimen, and thereby obtain its structural information. The varying acoustic impedance of tissues results in reflection of the probing ultrasound signal. The principle of time-of-flight is used to compute the acoustic impedance profile, and then the structure of the specimen. Unlike a radiation based-imaging modality such as X-ray computed tomography (CT), ultrasound poses fewer health hazards to patients due to its non-ionizing radiation. Hence, it is widely used in foetal imaging and analysis of cardiac motion. Ultrasound imaging is also widely used for non-destructive testing (NDT) of materials for fault diagnosis.
[0004] In all such imaging applications axial resolution of the image becomes an important factor as it determines the extent of utility of the obtained image. Axial resolution is generally understood as the ability to distinguish between targets aligned along the direction of propagation of the acoustic pulses. Relevance of the axial resolution is illustrated by FIG. 1, which depicts ultrasound reflections from three cracks 102, 104 and 106 of different widths in a metal block from a probing ultrasonic pulse 114. The corresponding reflected signalsare108, 110 and 112.As can be seen, reduction in axial distance between two faces of the crack brings the two corresponding reflected pulses close to each other to the extent that they overlap each other. Accordingly depending on the widths of the cracks, the reflected pulses may be well resolved 108, just-resolved 110, or unresolved 112. A standard ultrasound reconstruction technique will not be able to resolve the overlapping pulses. It can also be inferred from the illustration in FIG. 1 that the axial resolution of the ultrasound shall depend on the width of the probing pulse.
[0005] There are many other definitions available for axial resolution in ultrasound imaging literature. Hasegawa et al. defined the axial resolution of ultrasound imaging as the width at half-maximum of the probing pulse. In medical literature, Alexander and Swanevelder defined axial resolution of ultrasound as half the spatial pulse length (SPL) of the probing pulse. The axial resolution limit is principally governed by the quality factor (Q) of the transducer and the wavelength of ultrasound. Consider a transducer having quality factor , where is the center frequency and is the half-power bandwidth of the transmitted pulse. Righetti et al. showed that the axial resolution limit is given by:

(1)

where is the central wavelength and is a constant that depends on the exact definition of axial resolution. Typically, the constant takes a value between 1 and2. As D is inversely proportional to B, from Heisenberg's uncertainty principle, it is known that a pulse with a large frequency bandwidth has a small time duration and consequently a small axial resolution limit D. A Dirac impulse is the best probing pulse with the finest resolution. Any other pulse has a non¬zero pulse width and has a finite resolution limit given by (1).
[0006] Improvement of the axial resolution of ultrasound imaging is traditionally carried out by decreasing the SPL. The SPL is primarily dependent on the characteristics of the transducer. Oelze showed an improvement in the axial resolution of ultrasound imaging from 0.60 mm to 0.29 mm using a pulse compression technique. In recent literature, improvements in axial resolution using deconvolution based techniques have been reported. For example, Jensen reported an improvement in the axial resolution of a 3 MHz ultrasound signal from 0.581 mm to 0.116 mm using a Kalman filter-based deconvolution algorithm.
[0007] FIG. 2 illustrates a typical block diagram of present day ultrasound systems. A traditional ultrasound system consists of a probing device 202, an analog-to-digital converter (ADC) 204, signal processing unit 206, and a display unit 208. Typically, the probing device 202 consists of an array of transducers (64, 128, or 192 elements), which transmit ultrasound waves upon excitation. The transducers are excited according to a delay sequence such that the ultrasound waves are focussed at one point at the depth-of-focus (DOF). The process is repeated to focus along all the points of DOF to generate a sector scan. The reflected analog RF signals are sampled by theADC204 at or greater than the Shannon-Nyquist rate. The samples from ADC 204 are processed by the signal processing block 206 to generate an image, which is displayed on the screen of the display unit 208.
[0008] The sampling frequency is an important parameter in ultrasound imaging. The data storage space and processing time are proportional to the sampling frequency, determined by the Shannon the¬orem. Various methods for sampling and reconstruction of parametric analog signals exist in the literature. In this disclosure focus is on sub-Nyquist sampling techniques.
[0009] Vetterli et al. proposed finite-rate-of-innovation (FRI) signal sampling and reconstruction technique, which is applicable to non-bandlimited signals such as streams of Dirac impulses. The reconstruction problem is reduced to one of estimating the parameters of a sum of sinusoids, using Prony-type algorithms. Prony showed that the parameters of a small number of complex exponentials in noise can be estimated using number of samples that is directly proportional to the number of exponentials. This method is known as the annihilating filter technique and is used in FRI signal reconstruction. Prony's method gave rise to a number of methods for high-resolution spectrum estimation as well.
[0010] Several results extending the FRI signal sampling and reconstruction (referred to as FRI methodology hereafter) for larger class of signals have been reported in the past decade. Blu et al. revived and further developed an important subspace method originally proposed by Cadzow to enhance the performance of the annihilating filter in the presence of noise. Super-resolution for frequency-domain optical-coherence tomography (FDOCT) was demonstrated by Seelamantula and Mulleti. FRI signal sampling and reconstruction of ultrasound signals by sum-of-sincs (SoS) kernel was first shown by Tur et al. Compressed ultrasound imaging using Fourier-domain beamforming was proposed by Chernyakova et al.
[0011] However all the classical methods still require large data storage space and processing time. They also do not take in to account the structure of the reflected signal to reconstruct the image of the specimen with less number of samples. Use of an ADC with an order lesser sampling rate can significantly reduce the memory and computational requirements and thereby the cost of the system. For example, the cost of a 16-bit data acquisition (DAQ) card operating at a sampling frequency of 2 MHz is approximately Rs. 1, 24,000, whereas, a 16-bit DAQ card operating at 0.25 MHz costs only Rs. 45,000. The reduction in cost due to reduction of sampling frequency of ADC can have a direct bearing on the cost of the ultrasound scanner and make the diagnostic services affordable for large swath of disadvantaged population.
[0012] Furthermore, the known methods use straightforward reconstruction algorithms that results in poor resolution of the reconstructions and limited contrast.
[0013] There is, therefore, a need in the art for an efficient methodology for ultrasound image reconstruction in order to reduce the sampling rate at the data acquisition stage without effecting the quality of image.
[0014] All publications herein are incorporated by reference to the same extent as if each individual publication or patent application were specifically and individually indicated to be incorporated by reference. Where a definition or use of a term in an incorporated reference is inconsistent or contrary to the definition of that term provided herein, the definition of that term provided herein applies and the definition of that term in the reference does not apply.
[0015] In some embodiments, the numbers expressing quantities of ingredients, properties such as concentration, reaction conditions, and so forth, used to describe and claim certain embodiments of the invention are to be understood as being modified in some instances by the term “about.” Accordingly, in some embodiments, the numerical parameters set forth in the written description and attached claims are approximations that can vary depending upon the desired properties sought to be obtained by a particular embodiment. In some embodiments, the numerical parameters should be construed in light of the number of reported significant digits and by applying ordinary rounding techniques. Notwithstanding that the numerical ranges and parameters setting forth the broad scope of some embodiments of the invention are approximations, the numerical values set forth in the specific examples are reported as precisely as practicable. The numerical values presented in some embodiments of the invention may contain certain errors necessarily resulting from the standard deviation found in their respective testing measurements.
[0016] As used in the description herein and throughout the claims that follow, the meaning of “a,” “an,” and “the” includes plural reference unless the context clearly dictates otherwise. Also, as used in the description herein, the meaning of “in” includes “in” and “on” unless the context clearly dictates otherwise.
[0017] The recitation of ranges of values herein is merely intended to serve as a shorthand method of referring individually to each separate value falling within the range. Unless otherwise indicated herein, each individual value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g. “such as”) provided with respect to certain embodiments herein is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention otherwise claimed. No language in the specification should be construed as indicating any non-claimed element essential to the practice of the invention.
[0018] Groupings of alternative elements or embodiments of the invention disclosed herein are not to be construed as limitations. Each group member can be referred to and claimed individually or in any combination with other members of the group or other elements found herein. One or more members of a group can be included in, or deleted from, a group for reasons of convenience and/or patentability. When any such inclusion or deletion occurs, the specification is herein deemed to contain the group as modified thus fulfilling the written description of all Markush groups used in the appended claims.

OBJECTS OF THE INVENTION
[0019] An object of the present disclosure is to reduce cost of ultrasound imaging equipment.
[0020] Another object of the present disclosure is to provide an ultrasound imaging equipment that requires reduced data storage space and processing resources resulting in reduced cost of the ultrasound imaging equipment.
[0021] Another object of the present disclosure is to provide an ultrasound imaging equipment that operates at reduced sampling rate at data acquisition stage.
[0022] Yet another object of the present disclosure is to provide a methodology for ultrasound image reconstruction that can result in reduced sampling rate at data acquisition stage in an ultrasound imaging equipment.
[0023] Another object of the present disclosure is to reduce sampling rate at data acquisition stage in an ultrasound imaging equipment without deterioration in resolution and contrast of the ultrasound image.
[0024] Another object of the present disclosure is to achieve super-resolution in ultrasound imaging below the classical sampling limit with FRI signal sampling and reconstruction.
[0025] Another object of the present disclosure is to provide a methodology for ultrasound image reconstruction that takes in to account structure of the reflected signal to reconstruct the image of the specimen with less number of samples.
[0026] Another object of the present disclosure is to provide a methodology for ultrasound image reconstruction that takes into account asymmetry of the reflected ultrasound pulses.
[0027] Still another object of the present disclosure is to provide a specific FRI methodology for ultrasound image reconstruction in order to reduce the sampling rate at the data acquisition stage.

SUMMARY
[0028] Aspects of the present disclosure relate to ultrasound imaging. In particular, it pertains to a specific methodology for ultrasound image reconstruction that can enable reduction in sampling rate of the reflected ultrasonic pulses without effecting resolution and contrast of the reconstructed image. In an aspect, reduction in sampling rate can result in reduced requirement for data storage space and processing resources, which, in turn, can lead to considerable reduction in cost of the ultrasound imaging equipment.
[0029] In an aspect, the reduction in sampling rate is achieved by employing FRI signal sampling and reconstruction method. The ADC can be equipped with a suitable sampling kernel, such as a Non-Periodic Sum-of-Sincs (NP-SoS) sampling kernel, to observe the reflected RF analog signal and sample it at sub-Nyquist rate uniformly. Apart from uniform sampling, non-uniform sampling in a single or multiple channels in a multiplexed or interleaved fashion can also be done.
[0030] In another aspect of the present disclosure, the proposed methodology exploits the structure of the reflected signal to reconstruct the image of the specimen with less number of samples at sub-Nyquist sampling rates. At the same time, the quality of the reconstructed imageis comparable to the one obtained by classical ultrasound reconstruction techniques.
[0031] In another aspect of the disclosure, asymmetry in the reflected ultrasound pulses is modelled using the fractional Hilbert transform (FrHT) operator or derivative based asymmetry modelling. FRI modelling using FrHT or derivative based asymmetry modelling improves accuracy of parameter estimation and thus quality of the reconstruction.
[0032] In another aspect, the present disclosure provides a system for sampling the reflected or transmitted ultrasonic pulses and image reconstruction wherein the system may comprise a signal acquiring module configured to acquire reflected or transmitted ultrasonic pulses and sample them at sub-Nyquist rate; and a processing module configured to estimate time and amplitude parameters from the acquired samples of the reflected or transmitted ultrasonic pulses and reconstruct the image. In an aspect, the system of the present disclosure provides for the sampling and reconstruction employing finite-rate-of-innovation (FRI) signal sampling and reconstruction.
[0033] In an embodiment, the signal acquiring module can incorporate a transducer, which can be a single element transducer or can comprise an array of transducers with or without a transmit or receive beam forming.
[0034] In another aspect, the signal acquiring module further incorporates a sampling kernel selected from a group comprising non-periodic SoS kernel, sum of modulated raised cosine kernel, and sum of modulated spline kernel.
[0035] In another aspect, the reflected ultrasonic pulses are modelled as asymmetrical pulses using Fractional Hilbert Transform.
[0036] In another aspect, the processing module is configured to carry out parametric reconstruction of time delays and estimate amplitudes of the reflected ultrasonic pulses. In an aspect, the parametric reconstruction of the time delays is done by means of one of or combination of annihilating filter, matrix pencil method, or the method of estimation of signal parameters via rotational invariance technique, or their variants; and the amplitudes can be estimated using one of or a combination of linear least-squares, weighted least-squares regression, iterative weighted least-squares regression, Huber loss function, or their variants.
[0037] In another aspect, the proposed system results in reduced sampling rate without effecting the resolution and contrast of the reconstructed image which possesses super-resolution.
[0038] Various objects, features, aspects and advantages of the inventive subject matter will become more apparent from the following detailed description of preferred embodiments, along with the accompanying drawing figures in which like numerals represent like components

BRIEF DESCRIPTION OF THE DRAWINGS
[0039] The accompanying drawings are included to provide a further understanding of the present disclosure, and are incorporated in and constitute a part of this specification. The drawings illustrate exemplary embodiments of the present disclosure and, together with the description, serve to explain the principles of the present disclosure.
[0040] FIG. 1 illustrates a typical example a metal block with cracks of varying width and corresponding reflected ultrasonic pulses to show relevance of axial resolution.
[0041] FIG. 2 illustrates a typical block diagram of present day ultrasound systems.
[0042] FIG. 3 illustrates an exemplary block diagram of the proposed ultrasound systems in accordance with embodiments of the present disclosure.
[0043] FIG. 4 illustrates an exemplary block diagram of a kernel based generalized sampling scheme in accordance with embodiments of the present disclosure.
[0044] FIG. 5A to FIG. 5C illustrate exemplary impulse response of sampling kernels having an ideal low pass filter, a periodic SoS filter and a Non-periodic SoS filter respectively in accordance with embodiments of the present disclosure.
[0045] FIG. 6 illustrates an exemplary block diagram for wavelet denoising using undecimated Haar filterbank and two levels of decompositionaccordance with embodiments of the present disclosure.
[0046] FIG. 7A illustrates an exemplary image of one of the five double-layered specimens having thickness of 3% Agarose layer equal to mm in accordance with embodiments of the present disclosure.
[0047] FIG. 7B illustrates an exemplary schematic diagram indicating varying thickness of 3% Agarose layer in five double-layerd Agarose specimensin accordance with embodiments of the present disclosure.
[0048] FIG. 8A illustrates anexemplary image of a seven-layered Agarose specimen in accordance with embodiments of the present disclosure.
[0049] FIG. 8B illustrates a representative diagram indicating concentrations and dimensions of a seven layered Agarose specimen in accordance with embodiments of the present disclosure.
[0050] FIG. 9A and FIG. 9B illustrate exemplary block diagrams of the ultrasound imaging setup used during experiments and an exemplary image of the experimental set up used to image the Agarose phantom respectively in accordance with embodiments of the present disclosure.
[0051] FIG. 10 illustrates an exemplary image of JSR-DPR pulser-receiver used to image the Agarose phantomin accordance with embodiments of the present disclosure.
[0052] FIG.11A and FIG.11B illustrate exemplary pulse reflected from two-inches wide silica block, when illuminated with a V323 Olympusultrasound immersion transducer and the pulse shape modelled as a modulated Gaussian in accordance with embodiments of the present disclosure.
[0053] FIG. 12A to FIG. 12D illustrate the results obtained by imaging the specimen having 3% Agarose layer thickness of 1 mm as in FIG. 7Busing the proposed invention in accordance with embodiments of the present disclosure.
[0054] FIG. 13A to FIG.13E illustrate exemplary demodulated signal and boundaries estimated using FRI methodology in respect of samples having thicknesses of mm, mm, mm, mm, and mm respectively in accordance with embodiments of the present disclosure.
[0055] FIG.14A and FIG. 14B illustrate exemplary ultrasound reflections recorded from a multi-layered Agarose specimen using a 31 MHz analog-to-digital-converter (ADC); and the demodulated signal respectively in accordance with embodiments of the present disclosure..
[0056] FIG. 15A illustrates an exemplary reflector distribution of specimen with pins and cystsin accordance with embodiments of the present disclosure.
[0057] FIG. 15B to FIG. 15E illustrate exemplary original specimen sampledat 40 MHz, and FRI signal sampling and reconstruction withmodel order L of 80, 140, and 200 respectively in accordance with embodiments of the present disclosure.
[0058] FIG. 15F and FIG. 15G illustrate exemplary acoustic pulse used to probe the specimenand the 0 degree line from the 32 element in accordance with embodiments of the present disclosure.
[0059] FIG.15H to FIG. 15J illustrate exemplary reconstructions formodel order L = 80, 140, and 200 respectively in accordance with embodiments of the present disclosure.
[0060] FIG.16A illustrates an exemplary ultrasound imaging setup using an L&T Sonata LX ultrasound machine, Tektronix oscilloscope, and a wobbler transducer in accordance with embodiments of the present disclosure.
[0061] FIG.16B and FIG.16C illustrate exemplary images of heart and kidney of a goat used as specimens for ultrasound imaging using the FRI approach in accordance with embodiments of the present disclosure.
[0062] FIG.17A illustrates an exemplary standard reconstruction of the heart of a goat using a wobbler transducer at a sampling frequency of 12.25 MHz.
[0063] FIG.17B and FIG.17C illustrate exemplary FRI reconstruction of the heart of the goat using specimens at (a) a sampling frequency 0.7 MHz & L = 10, and (b) sampling frequency 1.01 MHz & L = 14 respectively in accordance with embodiments of the present disclosure.
[0064] FIG.18A illustrates an exemplary standard reconstruction of kidney of a goat using a wobbler transducer at a sampling frequency of 12.25 MHz.
[0065] FIG.18B and FIG.18C illustrate exemplary FRI reconstruction of the kidney of the goat using specimens at (a) a sampling frequency 0.7 MHz & L = 10, and (b) sampling frequency 1.01 MHz & L = 14 respectively in accordance with embodiments of the present disclosure.

DETAILED DESCRIPTION
[0066] The following is a detailed description of embodiments of the disclosure depicted in the accompanying drawings. The embodiments are in such detail as to clearly communicate the disclosure. However, the amount of detail offered is not intended to limit the anticipated variations of embodiments; on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the present disclosure as defined by the appended claims.
[0067] Each of the appended claims defines a separate invention, which for infringement purposes is recognized as including equivalents to the various elements or limitations specified in the claims. Depending on the context, all references below to the "invention" may in some cases refer to certain specific embodiments only. In other cases it will be recognized that references to the "invention" will refer to subject matter recited in one or more, but not necessarily all, of the claims.
[0068] Various terms as used herein are shown below. To the extent a term used in a claim is not defined below, it should be given the broadest definition persons in the pertinent art have given that term as reflected in printed publications and issued patents at the time of filing.
[0069] It is to be understood that though the embodiments of the present disclosure have been explained by their application to medical imaging, these can as well be applied to ultrasound or low or high-frequency acoustic wave-based non-destructive testing and evaluation of materials, equipment, or parts thereof.
[0070] Embodiments of the present disclosure relate to ultrasound imaging. In particular it pertains to a specific methodology for ultrasound image reconstruction that can enable reduction in sampling rate of the reflected ultrasonic pulses without effecting resolution and contrast of the reconstructed image. In an aspect, reduction in sampling rate can result in reduced requirement for data storage space and processing resources which in turn can lead to considerable reduction in cost of the ultrasound imaging equipment.
[0071] In an aspect, the reduction in sampling rate is achieved by employing FRI signal sampling and reconstruction method. The ADC can be equipped with a suitable sampling kernel, such as a non-periodic sum-of-sincs (NP-SoS) sampling kernel, to observe the reflected RF analog signal and sample it at sub-Nyquist rate uniformly.
[0072] Referring to FIG. 3 which illustrates an exemplary block diagram 300 of the proposed ultrasound system employing the proposed superresolved ultrasound image reconstruction methodology at sub-Nyquist sampling rates. The proposed ultrasound system can incorporate a signal acquisition stage comprising a transducer 302 and an ADC 304; and a digital processing unit 312 comprising a beam forming unit 306, a parameter estimation unit 308 and an image constructor 310.
[0073] In an aspect, the transducer 302 can be a single element transducer or can comprise an array of transducers with or without a transmit or receive beam forming.
[0074] In an embodiment, the ADC 304 can be equipped with a suitable sampling kernel, such as but not limited to a NP-SoS kernel that can reduce the sampling rate at which the ADC 304 operates. In an aspect this can reduce the amount of data acquired and hence the processing time and cost. The reduction in sampling rate is achieved by employing FRI signal sampling and reconstruction method.
[0075] The reflected RF analog signal corresponding to the acquired pulse is convolved with the sampling kernel and resulting function is observed through the sampling kernel and the resulting signal is sampled at sub-Nyquist rate uniformly. Apart from uniform sampling, nonuniform sampling in a single or multiple channels in a multiplexed or interleaved fashion can also be done.
[0076] The parameter estimation unit 308 can be configured to carry out parametric reconstruction of time delays and estimating amplitudes of the reflected ultrasonic pulses. In an aspect, the parametric reconstruction of the time delays is done by means of the annihilating filter, matrix pencil method, or the method of estimation of signal parameters via rotational invariance technique, or their variants; and the amplitudes can be estimated using linear least-squares, weighted least-squares regression, iterative weighted least-squares regression, Huber loss function, or their variants.
[0077] Since the proposed method employs FRI signal sampling and reconstruction method, the ultrasound imaging problem becomes an FRI signal sampling and reconstruction problem, which along with other embodiments of the disclosure, can be mathematically represented as follows:
Given measurements of
(2)
observed through a sampling kernel , estimate assuming that is known. The pulse transmitted is , s are the amplitudes of the reflected pulses and, s are the time delays of received pulses, which correspond to changes in acoustic impedance of the specimen under scan.
[0078] In an embodiment the disclosure shows that the FRI methodology enables modelling of the ultrasound reflections using localized pulses; and leads to super-resolved reconstruction of ultrasound images using sub-Nyquist sampling. The proposed FRI methodology is described in succeeding paragraphs.

FRI signal sampling and reconstruction
[0079] The Fourier transform of is
(3)

Consider the frequency-domain sequence

(4)

where and such that . Given for or more consecutive values of with the condition that , one can apply high-resolution spectral estimation (HRSE) methods to determine . Among the HRSE techniques, the annihilating filter (AF) method is widely deployed in FRI signal reconstruction. Since is known, can be computed a priori and hence, to compute , one has to estimate from .
.
[0080] The high-resolution parameter estimation problem in (2) is summarized in two steps as:
i. Compute the Fourier transform of at for , where is a set of consecutive integers with .
ii. Compute and estimate s and s by applying the AF method.

[0081] In practice, the pulse has finite support, which results in compact support for . For example, let the support of be given by , that is, for . The support of is . The frequency-domain samples are:

(5)

where and for , and zero elsewhere. Hence, given the basis functions for , can be computed from the inner products in (5). One can work within the sampling theory framework to estimate from .
[0082] FIG. 4 illustrates an exemplary block diagram of a kernel based generalized sampling scheme where is the impulse response of the sampling kernel. The goal is to design a sampling kernel and choose the sampling interval such that can be estimated from samples . The sampling frequency in radians is given by . The advantage of this approach is that can be computed from discrete-time Fourier transform (DTFT) of the sequence . The sampling kernel is designed to avoid the aliasing arising due to sampling at frequency locations for .
Sampling kernels
[0083] Compact support of results in infinite support of . Vetterli et al. proposed an ideal lowpass filter with cutoff frequency radians to remove the aliasing effect at the desired frequency provided that the sampling rate is greater than radians/second. Due to the non-compact support of the impulse response and its ideal behavior, implementation of the method is not practically feasible. Impulse response of the ideal lowpass filter is shown in FIG. 5A
[0084] If the support of the filter is limited to be finite, has infinite support and hence aliasing will affect the estimation of the frequency-domain samples. If the sampling kernel is designed such that aliasing at is zero for , one can estimate from . Tur et al. proposed a compactly supported kernel with frequency response of sum-of-sincs (SoS) for periodic FRI signals with period . In this setting, is chosen as . The impulse response and the frequency response of the SoS kernel are given as

(6)
(7)

respectively, with . Tur et al. assumed that . For aperiodic FRI signals, a repetition of the SoS kernel is proposed and the periodic-SoS (P-SoS) kernel is given as:

(8)

where the number of repetitions depends on support of the FRI signal . In (15), is chosen such that . Impulse response of the P-SoS filter, for and NP-SoS filter, are shown in FIG. 5B and FIG. 5C, respectively.
[0085] Proposed non-periodic SoS (NP-SoS) kernel: In an embodimnt, the present disclosure provides for a non-periodic SoS kernel for non-periodic FRI (NP-FRI) signals. In practice, the support of is not known a priori as it depends on the unknown delays s. Succeeding paragraphs show that the SoS kernel in (6), with a fixed support and without repetitions, can be used to estimate from the sampled signal . The Fourier transform of the sampled signal at is given as

(9)

where the sampling interval is chosen such that for .
Using in (9)

(10)
For and gives:

(11)

Hence, given the samples , can be computed as

(12)

The preceding results are summarized in the following theorem.
.
Theorem 1 The samples of the Fourier transform of at frequencies for can be computed from samples of the filtered signal by using the sampling kernel . The sampling rate should be , . The frequency-domain samples are computed from the samples of the filtered signal as , where .
Theorem 1 is not limited only to FRI signals but applicable to any .

[0086] Other sampling kernels: In an embodiment, it is possible to use other kernels such as those mentioned below in place of NP-SoS sampling kernel.
• Sum-of-modulated spline (SMS) kernels:

The impulse response of the SMS kernel is given by
(13)
where is -order B-spline.
The Fourier transform of the kernel in (13) is given by
(14)
which decays much faster than the SoS kernel, but the corresponding time support increases.

• Sum-of-modulated raised-cosine (SMRC) kernels:

The impulse response of the SMRC kernel is given by
(15)

where is defined as

The Fourier transform of the kernel in (15) is given by
(16)

Estimation of amplitudes and delays from the Fourier coefficients
[0087] The samples of the Fourier transform of at frequencies for are computed as stated in Theorem 1. From the Fourier coefficients

(17)

the problem of estimating is solved by using standard high-resolution
spectral estimation (HRSE) techniques such as the annihilating filter (AF), matrix-pencil method, minimum-norm method, estimation of signal parameters via rotational invariance technique (ESPRIT), etc. In the FRI literature, the annihilating filter is the most commonly used technique since it requires minimal number of measurements.

[0088] Estimation of delays: Annihilating filter: Consider a length- signal that is a sum of complex exponentials

(18)

Consider a finite-length causal filter , defined over . The convolution output , for is

If , then for . The -transform of a filter with zeros at is

(19)

There are unknown zeros of , thus . To solve the system of equations

(20)

at least equations are needed or . Hence, samples of are sufficient to estimate . The system of equations in (20) are compactly written in matrix form as

(21)

where

and is the ( length null vector.

[0089] Estimation of amplitudes: The linear system of equations given in (18) is compactly represented as , where , , and , and .
• Linear least-squares solution: After computing s, s are evaluated by solving the system of linear equations in (18). This gives the estimates of amplitudes in the least-squares sense.
• Iteratively reweighted least-squares (IRLS): IRLS regression can be used to get maximum-likelihood estimates of the amplitudes in presence of non-Gaussian noise. Given the system of equations , to find that minimizes the -norm for the linear regression problem,
(22)
The IRLS algorithm at iteration involves solving the weighted linear least squares problem:
(23)

where weights at iteration are updated as .

• Huber loss function: One could also use the Huber loss function or its variants for estimating the amplitudes to combat non-Gaussian noise. The Huber loss function is given by

where . The advantage of using the Huber loss function in estimation is that for small errors in the estimates, the -norm of the error is minimized whereas for outliers, the -norm is minimized.
[0090] These alternative estimation techniques increase the estimation accuracy of amplitudes in presence of non-Gaussian noise over the standard least-squares solution.
[0091] Denoising for pre-processing: In practice, the Fourier samples of the FRI signal are corrupted by noise. In an embodiment, prior to estimation of delays, the Cadzow denoising technique is used, which is an iterative method and converges in a small number of iterations (typically 10-15). Cadzow denoising employs singular value decomposition. Apart from Cadzow denoising, it is possible to denoise each scan-line separately by employing wavelet-based denoising techniques, preferably in a risk minimization framework. In an embodiment, the disclosure provides for use of undecimated wavelet transform (UWT) with shrinkage parameters for each subband as the denoising function. In an aspect, the proposed wavelet transform based method described in this invention is adventageous as it relies on the knowledge of only first- and second-order noise statistics and is independent of the noise probability distribution.
• Risk-estimation-based denoising
Considering a generic denoising problem for a signal in additive white noise:
(24)
The white noise assumption is without loss of generality. The goal is to estimate given . It is assumed that the first- and second-order statistics of the noise are known. The probability distribution of the noise may be unknown. The noise vector is assumed to have mutually uncorrelated entries with zero mean and finite variance . Let be the denoising function that estimates given as

The goal is to obtain the optimal denoising function such that the MSE between and given by is minimized:

(25)

The disclosure proposes a linear, shift-invariant function to denoise . Further, level undecimated wavelet transform is used as the denoising function. The overall transform-domain process shown in FIG. 6 is represented as

(26)
where and are reconstruction and decomposition filter matrices respectively, for the channel, , and is the column-stacked matrix of . The third term in (25) becomes



(27)
The first term in (25) becomes

Substituting (26), (27) and (28) in (25) gives
(28)
An unbiased estimate of (26) is
(29)
To estimate the parameters s in (29), gradient of with respect to is set to zero, which yields



(30)
The denoised estimate is computed as .
FRI modelling of asymmetric pulses
[0092] In an embodiment, the methodology proposed by the present disclosure provides for exploiting the structure of the reflected signal to reconstruct the image of the specimen with less number of samples at sub-Nyquist sampling rates. In an aspect, the quality of the reconstructed image remains comparable to the one obtained by classical ultrasound reconstruction techniques with the proposed methodology.
[0093] In an aspect of the disclosure, the structure exploited is asymmetry in the reflected ultrasound pulses. On probing a specimen having a generic acoustic impedance profile, the pulses in the reflected ultrasound signal are distorted apart from being shifted and scaled. For example, the distortion may change the width or asymmetry of the pulse. In such a case, a signal model with a higher number of degrees of freedom is required.
[0094] In an embodiment, the reflected ultrasound pulses are modelled using the fractional Hilbert transform (FrHT) operator. FRI modelling using the FrHT improves accuracy of parameter estimation and thus quality of the reconstruction.
[0095] Fractional Hilbert transform (FrHT) based asymmetry modelling: The ultrasound reflections from a specimen having piecewise-constant acoustic impedance was earlier reduced to (2). The reflected signal denotes a stream of pulses where the pulse is scaled by and shifted by . In asymmetrical modelling the signal is modelled as
(31)
where is an asymmetric distortion of specified by the distortion function and the parameter . The distortion function used is the FrHT. The FrHT of is

(32)
where is the fractional angle, is the Hilbert transform of , and is the FrHT kernel. Analogous to the Hilbert transform, the fractional Hilbert transform is a phase shifter. It advances the phase of negative frequencies by and retards the phase of positive frequencies by .
[0096] In an embodiment, a train of asymmetric pulses is modelled as an FRI signal using FrHT as follows

(33)

where each pulse has three degrees of freedom, time-location, amplitude, and asymmetry factor.
[0097] Derivative-based asymmetry modelling: In this model, the differentiation operator, much like the Hilbert operator, is used to model asymmetry. The signal consisting of asymmetric pulses is given by
(34)
where is constructed as follows
(35)
By changing and , pulses of varying degrees of asymmetry can be generated.
[0098] Reconstruction of FRI signals modelled by FrHT: The Fourier transform of in (33) is

(36)

where . Considering and as a set of consecutive positive integers such that , the disclosure proposes to construct

(37)
This can lead to construction:
(38)

[0099] Equation (38) is a frequently encountered model in FRI signal sampling and reconstruction of a stream of pulses. HRSE techniques can be used to estimate the parameters from the frequency samples . Computation of the Fourier samples from samples of is the same as that described in the paragraph [0085] dealing with Non-periodic SoS kernel.The disclosure proposes use of a HRSE technique to determine from in (38). Specifically, the annihilating filter is used to estimate , since it requires the least number of samples of in (38). On calculating , the amplitudes are obtained as the least-squares solution of the linear system of equations in (38). From (37), the amplitude and asymmetry factors of the pulses are given by

(39)
respectively, for .

[00100] Reconstruction of FRI signals modelled by the derivative operator: The Fourier transform of in (34) is . For and a set of consecutive integers , chosen such that the disclosure defines

(40)

[00101] In an embodiment, computation of the Fourier samples is carried out using the NP-SoS sampling kernel. A modified annihilating filter proposed in the disclosure is used to estimate . are estimated by solving a system of linear equations.
[00102] Modified annihilating filter: The problem of determining in (40) can be paraphrased into one of finding given
(41)
where are the unknown amplitudes of the exponentials. To solve for
from , the following proposition is made:
Proposition 1: The signal , where and , is annihilated by the filter, .
Proof. The filter, can be expanded as, , with filter coefficients . The output on filtering with , for is given by

Thus, the filter annihilates the signal .
[00103] Using the above proposition in (40), annihilates the sequence , when . The roots of the filter are with multiplicity two. To ensure there is no warping in the computation of , the disclosure provides for choosing .
[00104] In another aspect, the present disclosure provides a system for sampling the reflected or transmitted ultrasonic pulses and image reconstruction wherein the system can comprise a signal acquiring module configured to acquire reflected or transmitted ultrasonic pulses and sample them at sub-Nyquist rate; and a processing module configured to estimate time and amplitude parameters from the acquired samples of the reflected or transmitted ultrasound pulses and reconstruct the image. In an aspect, the system of the present disclosure provides for the sampling and reconstruction employing finite-rate-of-innovation (FRI) signal sampling and reconstruction.
[00105] In an embodiment, the signal acquiring module can incorporate a transducer which can be a single element transducer or can comprise an array of transducers with or without a transmit or receive beamforming.
[00106] In another aspect, the signal acquiring module can further incorporate a sampling kernel selected from a group comprising non-periodic SoS kernel, sum of modulated raised cosine kernel, and sum of modulated spline kernel.
[00107] In another aspect, the reflected ultrasonic pulses are modelled as asymmetrical pulses using fractional Hilbert transform.
[00108] In another aspect, the processing module is configured to carry out parametric reconstruction of time delays and estimate amplitudes of the reflected ultrasonic pulses. In an aspect, the parametric reconstruction of the time delays is done by means of any or combination of annihilating filter, matrix pencil method, or the method of estimation of signal parameters via rotational invariance technique, or their variants; and the amplitudes can be estimated using any or a combination of linear least-squares, weighted least-squares regression, iterative weighted least-squares regression, Huber loss function, or their variants.
[00109] In another aspect, the proposed system results in reduced sampling rate without effecting the resolution and contrast of the reconstructed image which possesses super-resolution.

EXPERIMENTS
[00110] In an embodiment, the proposed NP-SoS kernel is used to sample the reflected ultrasound pulsed signal at sub-Nyquist rate and their reconstruction was studied. In first of such experimental studies a synthetic Agarose phantom was used to investigate the super-resolution properties of the FRI sampling and reconstruction technique using the NP-SoS kernel. In second of these experimental studies, simulation results of the proposed system obtained using Field-II imaging software have been disclosed. Finally, results of imaging the heart and kidney of a goat using the proposed invention are presented.

Axial super-resolution
[00111] Two sets of experiments were carried out to ascertain axial resolution. In the first experiment, a set of five double-layered specimens as shown in FIG. 7B were used. Each of the double-layered phantoms has a Agarose layer on top of a Agarose layeras shown in FIG. 7A. Thicknesses of the Agarose layers was kept as mm, mm, mm, mm, and mm as illustrated in FIG. 7B. The objective of this experiment was to determine the thickness of the Agarose layer that can be resolved using the proposed methodology. Performance of the proposed methodologywas compared with the theoretical axial-resolution limit for ultrasound imaging.
[00112] In the second experiment, a specimen with varying acoustic impedance was used. FIG. 8Aillustrates animage of the specimen and FIG. 8Billustrates concentrations and geometric dimensions. It consists of alternating concentration and concentration Agarose layers. The thickness of the layer starts with 2 mmand and goes up to mm, while the layer is maintained at a constant mm thickness. In an aspect, this specimen mimics the realistic scenario of varying acoustic impedance resembling various constituents of human body such as skin, fat, muscle, and bone.
[00113] Experimental setup: An exemplary block diagram illustrating schematic of the ultrasound imaging setup used during experements is shown in FIG. 9A. FIG. 9B illustrates an exemplary image of the experimental set up used to image the Agarose phantom. An Olympus V ultrasound immersion transducer with center frequency MHz was used to image the Agarose specimens. A JSR-DPR pulser-receiver illustrated in FIG. 10 was used to trigger the transducer and condition the reflected signal. The operational settings of the pulser-receiver used in this experiment are given in Table 1 below. The reflected pulse was acquired using a Tektronix digital phosphor oscilloscope (DPO) (DPO2014B) at a sampling frequency of MHz.
Parameter Setting
Mode Echo
Relative gain 30 dB
High-pass filter 1 MHz
Low-pass filter 35 MHz
Trigger Internal
Damping 2
Pulse amplitude 5
Pulse energy 4 (high)
PRF rate 6

Table 1:The settings of the pulser-receiver used to image the Agarose phantoms.

[00114] A pulse generated by the immersion transducer as given in the manufacturer’s manual is shown in FIG. 11A. The pulse or point spread function/impulse response of the transducer is used directly or modelled with the kernel that is having an analytical expression such as Gaussian, modulated Gaussian, or their truncated versions, polynomial splines, as asymmetric kernel modelled using the fractional Hilbert transform, etc. For the purpose of illustration, the pulse is modelled as a modulated Gaussian and is truncated appropriately
(42)

where Hz, s, and as shown in FIG. 11B. The variance of the Gaussian and phase of the sinusoid are obtained experimentally by least-squares fitting.

[00115] Experimental results: The results obtained by imaging the specimens shown in FIG. 7Aand FIG. 7B using the proposed invention are illustrated in FIG. 12A to FIG. 12D whereinFIG. 12A shows the reflected ultrasound signal from the mm thickness specimen acquired using the DPO. As can be seen there are three peaks in the reflected signal, where the first one is due to the change of impedance in the path of propagation of ultrasound from water to the Agarose layer. The second reflection is due to the boundary between the Agarose and Agarose layers, and the third reflection is due to the boundary between Agarose layer and water. The reflected signal is of the form
(43)
where , as shown in FIG. 12D. Using the Bedrosian theorem for approximating the Hilbert transform of , the demodulated reflected signal is given by
(44)
The proposed NP-SoS sampling kernel is applied with and as shown in FIG. 12C. Due to presence of acquisition noise, the signal needs to be oversampled to obtain a high-resolution reconstruction. Hence, a large-sized frequency set is used in this setup. The corresponding sampling frequency according to Theorem 1, is MHz. To further suppress acquisition noise, iterative Cadzow algorithm is employed on the Fourier-domain samples. The AF technique is applied on the Fourier samples obtained in (17) to estimate the locations of the pulses. The amplitudes are estimated from the least-squares solution of the resulting Vandermonde system of equations in (17). The estimated peaks are shown in FIG. 12D. The FRI sampling and reconstruction algorithm is applied to specimens of thicknesses mm, mm, mm, mm, and mm. Demodulated signal and boundries estimated using FRI methodology in respect of these samples are illustrated in FIG.13A to FIG.13E. To demonstrate repeatability of the algorithm, five measurements were taken on each of the specimen. Estimation for thickness of the layer is done by taking average of the five measurements. A comparison of the estimated thickness of the Agarose specimen against the ground truth along with the standard deviations across measurements are presented in Table 2 below:

Sample Ground truth
(mm) Estimate
(mm) Standard deviation (mm)
1 1.88 1.8627 0.0406

2 1 1.0068 0.172

3 0.80 0.8140 0.0334

4 0.33 0.3334 0.0242

5 0.25 0.3734 0.0722

Table 2:Comparison of the estimated thickness from five measurements of the Agarose

[00116] The axial resolution is an important parameter for elastographic studies using ultrasound imaging. For the Olympus V transducer, . The wavelength of the transducer is m, and the velocity of ultrasound in Agarose is m/s. Using a proportionality constant , the axial resolution limit evaluates to mm for our experimental setup.
[00117] Table 2 shows that the FRI algorithm is capable of resolving layers/interfaces that are spaced mm apart, which is about three times below the conventionally established limit of mm. From Table 2, it can be observed that the algorithm ceases to super-resolve when the thickness of the layer goes below mm.
[00118] Study on composite specimen: FIG. 14A illustrates the ultrasound reflection when the composite specimen shown in FIG. 8A is imaged using an immersion transducer. The demodulated reflected signal is given in FIG. 14B. As the specimen consists of eight boundaries, estimatation of the peaks of the signal can be done assuming that the model order . A NP-SoS kernel with radians/s is used to estimate the spectral samples. To counter acquisition noise, we set = . The signal is acquired after filtering with an SoS kernel at a sampling frequency of MHz. The iterative Cadzow denoising technique is employed to denoise the spectral samples. The peaks estimated using the annihilating filter technique are shown in FIG. 14B. It can be seen that out of eight, seven peaks are identified accurately. The last peak at a depth of mm is wrongly placed at a depth of mm. This is because the ultrasound signal at a depth of mm is highly attenuated. In fact, the amplitudes at this depth are comparable to the noise amplitude.

Field-II simulations
[00119] In an embodiment, the proposed NP-SoS kernel is applied on a two-dimensional pins and cyst specimen generated using Field II software. Field II is used to simulate ultrasound pressure fields using linear acoustics. It is based on Tupholme and Stepanishen’s method to calculate pulsed ultrasound fields. Pins and cysts simulate ultrasound scatterers in the human body. Pins simulate the high-reflective regions in the body such as bones, while cysts simulate the low-reflective, high absorption regions such as blood and water. FIG.15A illustrates an exemplary reflector distribution of specimen with pins and cysts in accordance with embodiment of the present disclosure.
[00120] A 64-element linear ultrasound transducer array is simulated to produce the ultrasound signal and acquire the measurements. The probing pulse, has a center frequency of MHz. Eighty one beams are acquired by each of the elements at a sampling frequency of MHz. Since these signals are in the radio-frequency (RF) range, the measurements are referred to as RF data. The RF data is beamformed using the sum-and-delay beamformer. The experiment was conducted to show the FRI reconstruction on a specimen consisting of both pins and cysts. The signal acquired at a sampling frequency of MHz is shown in FIG.15B.
[00121] FIG.15C to FIG.15E illustrate an exemplary original specimen sampled using FRI signal sampling and reconstruction model order L of 80, 140, and 200 respectively in accordance with embodiment of the present disclosure.At a model order of , all the pins have been accurately recovered, while the central cyst at a depth of mm is not captured. The spreading is due to the scatterers around a depth of mm, which causes the cyst to be diffused in the reconstruction.
[00122] FIG.15F and FIG.15G illustrate exemplary acoustic pulse used to probe the specimen and the 0 degree line from the 32 element in accordance with embodiment of the present disclosure.Reconstructions formodel order L = 80, 140, and 200 is illustrated in FIG.15H to FIG.15J respectively.

Imaging of medical specimens
[00123] Heart and kidney of a goat was imaged using the proposed methodology on a Larsen and Toubro (L&T) Sonata LX ultrasound machine. The ultrasound probe consisted of a single element wobbler transducer operating at MHz. The experimental setup used is shown in FIG.16A. To reconstruct the image, the methodology proposed in the invention is applied to each scan line (A-mode reconstruction). B-mode ( -D mode) sector scan image is constructed by combining all the A-mode scan reconstructions. The B-mode reconstructions can be stacked and rendered in case of -D volumetric imaging.
[00124] FIG.16B illustrates the heart of goat subjected to imaging using the proposed methodology. The standard reconstruction obtained at a sampling frequency of MHz and depth setting of cm is shown in FIG.17A. The sector angle is set to and the number of RF lines in one sector sweep is . The image was reconstructed using the methodology proposed in the invention at model orders (sampling frequency of MHz) and (sampling frequency of MHz). The corresponding reconstructions are shown in FIG.17B and FIG.17C. In comparison to the reconstruction at MHz, the chambers of the heart are more clearly highlighted in the FRI reconstruction. Further, the reconstructions are achieved by operating at a sampling frequency which is twelve times smaller than the standard sampling frequency used in FIG.17A.
[00125] FIG.16C illustrates the kidney of goat subjected to imaging using the proposed methodology a depth setting of cm and a sector angle of . As a variation from the heart specimen, the kidney is imaged by placing it in water to reduce the speckle noise at data acquisition stage. The standard reconstruction at a sampling frequency of MHz is shown in FIG.18A. This reconstruction consists of fewer speckles in comparison to the heart specimen. The bean shaped outline of the kidney is also visible in the standard reconstruction. The kidney ultrasound image was reconstructed using the methodology proposed in the invention at model orders of (sampling frequency of MHz) and (sampling frequency of MHz). The corresponding reconstructions are shown in FIG.18B and FIG.18C. The outline of the kidney and the internal structure are sharper in the case of the proposed reconstructions in comparison with the standard reconstruction. Also, the sampling frequency is reduced by a factor of twelve.
[00126] While the foregoing describes various embodiments of the invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof. The scope of the invention is determined by the claims that follow. The invention is not limited to the described embodiments, versions or examples, which are included to enable a person having ordinary skill in the art to make and use the invention when combined with information and knowledge available to the person having ordinary skill in the art.

ADVANTAGES OF THE INVENTION
[00127] The present disclosure reduces cost of ultrasound imaging equipment.
[00128] The present disclosure provides an ultrasound imaging equipment that requires reduced data storage space and processing resources resulting in reduced cost of the ultrasound imaging equipment.
[00129] The present disclosure provides an ultrasound imaging equipment that operates at reduced sampling rate at data acquisition stage.
[00130] The present disclosure provides a methodology for ultrasound image reconstruction that can result in reduced sampling rate at data acquisition stagein an ultrasound imaging equipment.
[00131] The present disclosure reduces sampling rate at data acquisition stagein an ultrasound imaging equipment without deterioration in resolution and contrast of the ultrasound image.
[00132] The present disclosure achieves super-resolution in ultrasound imaging below the classical sampling limit with FRI signal sampling and reconstruction.
[00133] The present disclosure provides a methodology for ultrasound image reconstruction that takes in to account structure of the reflected signal to reconstruct the image of the specimen with less number of samples.
[00134] The present disclosure provides a methodology for ultrasound image reconstruction that takes into account asymmetry of the reflected ultrasound pulses.
[00135] The present disclosure provides a specific FRI methodology for ultrasound image reconstruction in order to reduce the sampling rate at the data acquisition stage.