Description:FORM 2

THE PATENTS ACT, 1970
(39 of 1970)
&
THE PATENT RULES, 2003

COMPLETE SPECIFICATION
(See Section 10 and Rule 13)

Title of invention:
ATTRACTOR RECONSTRUCTION APPROACH FOR RESPIRATION RATE ESTIMATION

Applicant:
Tata Consultancy Services Limited
A company Incorporated in India under the Companies Act, 1956
Having address:
Nirmal Building, 9th Floor,
Nariman Point, Mumbai 400021,
Maharashtra, India

The following specification particularly describes the invention and the manner in which it is to be performed.
TECHNICAL FIELD
The disclosure herein generally relates to the field of a respiration rate estimation, and more particularly, a method and system for respiration rate estimation from Photoplethysmogram (PPG) signal using an Attractor Reconstruction (AR) approach.

BACKGROUND
Respiratory Rate (RR) is an essential and critical parameter in clinical care as it provides valuable information about an individual’s health status and has been integrated with many disease guidelines for early diagnosis. For example, the elevation of RR >40 breaths/min (BPM) in infants is considered a clinical red flag for pneumonia. Similarly, an elevated RR in adults indicates significant respiratory distress. Thus, RR is monitored in primary care to detect chronic obstructive pulmonary diseases like pneumonia, sepsis, hypercarbia, and pulmonary embolism, and may necessitate urgent medical intervention. Various methods exist to monitor the respiration rate, like capnography, inductance plethysmography, spirometer, impedance plethysmography (used in hospitals), and inductance plethysmography sensors. However, most of these techniques are time-consuming, inaccurate, and poorly carried out. Furthermore, it is uncomfortable as it must be worn around the chest or as a mask. Therefore, there is a demand for wearable sensing, which aids remote and continuous monitoring.
In this context, various research groups studied and used the PPG signal to monitor the cardiac system and general wellness by estimating the heart rate (HR), respiration, blood pressure (BP), biomarker for cardiovascular health and diagnosis. Besides this, PPG sensor usage in other physiological parameters like epileptic seizures, mental stress, sleep monitoring, blood glucose, and drug delivery monitoring. Thus, it is clear that the clinical and research community has widely accepted PPG as a source of the non-invasive technique commonly used and also to measure RR. Despite its non-invasive nature and ability to provide continuous monitoring, the PPG signal quality is a significant concern. PPG signals are prone to various sources of noise like inter-biological variation such as skin tone, obesity, age, and gender and intra-biological variabilities such as respiration, body temperature, site of measurement, and external factors such as motion artifact, the pressure between the sensor and the skin, and type of sensors.
Ever since AR was first applied in the biological signal by Takens, 1981 (Detecting strange attractors in aid turbulence, Dynamical Systems and Turbulence, F.Takens, 898 (1981), 366). It has been applied by various applications like heart rate (HR) (Measurement of cardiovascular state using attractor reconstruction analysis, 2015 23rd European Signal Processing Conference (EUSIPCO), IEEE, 2015, P. H. Charlton, L. Camporota, J. Smith, M. Nandi, M. Christie, P. J. Aston, R. Beale, IEEE, 2015, pp. 444–448); blood pressure (BP) (Comparison of attractor reconstruction and HRV methods for analysing blood pressure data, Computing in Cardiology, P. J. Aston, M. Nandi, M. I. Christie, Y. H. Huang, IEEE, 2014, pp. 437–440); and EEG time series data (Research on the relation of EEG signal chaos characteristics with high-level intelligence activity of human brain, Nonlinear biomedical physics 4 (2010) 2, X. Wang, J. Meng, G. Tan, L. Zou ). AR is also used for feature extraction (Obstructive sleep apnea detection with nonlinear analysis of speech, Biomedical Signal Processing and Control 84 (2023) 104956, D. Yilmaz, M. Yildiz, Y. U. Toprak, S. Yetkin); analyzing the signal morphology in a specific environment or a diseased state (Atrial fibrillation detection using convolutional neural net- works on 2-dimensional representation of ECG signal, Biomedical Signal Pro- cessing and Control 74 (2022) 103470., B. Kr ´ol-J ´ozaga); signal quality assessment (Photoplethysmography signal quality assessment using attractor reconstruction analysis, Biomedical Signal Processing and Control 86 (2023) 105142, J. Schmith, C. Kelsch, B. C. Cunha, L. R. Prade, E. A. Martins, A. L. Keller, R. M. de Figueiredo). Thus, these advantages make AR-based techniques more suitable for human vital parameter estimation from wearable devices.
Many optimization techniques were proposed to effectively choose the delay (Determining respiratory rate from Photoplethysmogram and electrocardiogram signals using respiratory quality indices and neural networks, Plos one 16 (4) (2021) e0249843, S. Baker, W. Xiang, I. Atkinson), (Monitoring of respiratory rate in postoperative care using a new photoplethysmographic technique, Journal of clinical monitoring and computing 16 (2000) 309–315., L. Nilsson, A. Johansson, S. Kalman), (Photoplethysmography-based respiratory rate estimation algorithm for health monitoring applications, Journal of Medical and Biological Engineering 42 (2) (2022) 242–252. T. Iqbal, A. Elahi, S. Ganly, W. Wijns, A. Shahzad). On the other hand, even without optimization, the delay was considered as 1/3rd of the average cycle length of the PPG signal (Multiparameter respiratory rate estimation from the photoplethysmogram, IEEE Transactions on Biomedical Engineering 60 (7) (2013) 1946–1953., W. Karlen, S. Raman, J. M. Ansermino, G. A. Dumon ), (Toward a robust estimation of respiratory rate from pulse oximeters, IEEE Transactions on Biomedical Engineering 64 (8) (2016) 1914–1923. M. A. Pimentel, A. E. Johnson, P. H. Charlton, D. Birrenkott, P. J. Watkin- son, L. Tarassenko, D. A. Clifton) Here, the naturally occurring baseline variation is separated from the PPG signal by projecting the attractor onto a phase space using a delay coordinate from which new quantitative measures are obtained. The AR technique supports the multi- parameter estimation by segregating the low frequency DC component from high frequency AC component.
To overcome the above limitations, many research groups are working to extract the respiration signal and to estimate the RR from PPG, which can be categorized into three categories. First category, the filter-based technique to extract the respiratory signal from PPG signal. Second category, feature-based techniques that extract features like amplitude, width, height, and so from the PPG signal. Third category is domain transformation like frequency domain like Fourier transform, auto-regression, Welch method, joint time-frequency method. Despite this, a wide gap exists in standard pre-processing frameworks such as data recording duration, segmentation, filtering, and smoothing technique. In addition, the above techniques face the following limitations in RR estimation: a) Discarding the vital information, estimating the signal quality either manually or automatically using signal quality index (SQI) and discarding the windowed PPG to improve the accuracy of RR estimation; and b) Need of external sensors to remove the noise in the PPG for RR using additional sensors like accelerometer, and pressure sensor.

SUMMARY
Embodiments of the present disclosure present technological improvements as solutions to one or more of the above-mentioned technical problems recognized by the inventors in conventional systems. For example, in one embodiment, a method for respiration rate estimation from PPG signal using an attractor reconstruction approach is provided. The processor-implemented method includes receiving, via an Input/Output (I/O) interface, a pre-defined raw Photoplethysmography (PPG) signal x_PPG (t) as input, wherein x_PPG (t) denotes a time series of a windowed PPG signal of a pre-defined duration. A delay value (t) is calculated for the received raw PPG signal x_PPG (t) to obtain a three-dimensional (3D) phase space signal x_3,1 (t), x_3,2 (t), x_3,3 (t) using a pre-defined delay technique and based on at least one of the below mathematical equations-
x_3,1 (t)= x_PPG (t); x_3,2 (t)=x_PPG (t- t) =x_3,1 (t- t); and x_3,3 (t)=x_PPG (t- 2t) =x_3,1 (t- 2t).
Further, one or more low frequency components are separated from one or more high frequency components of the signal x_3,1 (t), x_3,2 (t), and x_3,3 (t) by undergoing a transformation to obtain three signals u(t),v(t) and w(t) using the unit vectors V_3,1, V_3,2 and V_3,3, wherein the one or more low frequency components comprises a low frequency signal u(t) that includes noise. The low frequency signal u(t) is converted to frequency domain by passing the low frequency signal u(t) through the Band-Pass Filter (BPF) and applying frequency domain transform like a Fourier Transform technique, wherein a frequency having the maximum power is estimated as the frequency of the Respiration Rate (RR), which is estimated ?RR?_in (i). Finally, performing a post-processing by invoking a retract module which reduces the fluctuation in the Respiration Rate (RR) estimates when the difference between the Respiration Rate (RR) estimates of any two successive windowed PPG signals exceeds 2 breaths/min (BPM) using an outline elimination technique, wherein the outline elimination technique uses a polynomial fit function.
In another embodiment, a system for respiration rate estimation from PPG signal using an attractor reconstruction approach is provided. The system comprises a memory storing a plurality of instructions, one or more Input/Output (I/O) interfaces, and one or more hardware processors coupled to the memory via the one or more I/O interfaces. The one or more hardware processors are configured by the instructions to receive, via an Input/Output (I/O) interface, a pre-defined raw Photoplethysmography (PPG) signal x_PPG (t) as input, wherein x_PPG (t) denotes a time series of a windowed PPG signal of a pre-defined duration.
One or more input hardware could be a wearable device, or the sensor device can be referred interchangeably in the disclosure. The wearable device is also configured to transmit the result of monitoring to a remote destination through wireless communication for medical assistance. The wearable device is adapted to acquire PPG using non-contact (in a partially or fully) sensing mechanism or in contact with optical sensing or piezo- electrical technique or diaphragm technique or video-based sensing. The wearable device is configured to monitor or determine the health and wellness of humans, in the real time.
Further, the one or more hardware processors are configured by the instructions to calculate a delay value (t) for the received raw PPG signal x_PPG (t) to obtain a three-dimensional (3D) phase space signal x_3,1 (t), x_3,2 (t), x_3,3 (t) using a pre-defined delay technique and based on at least one of the below mathematical equations-
x_3,1 (t)= x_PPG (t); x_3,2 (t)=x_PPG (t- t) =x_3,1 (t- t); and x_3,3 (t)=x_PPG (t- 2t) =x_3,1 (t- 2t).
Furthermore, the one or more hardware processors are configured by the instructions to separate one or more low frequency components from one or more high frequency components of the signal x_3,1 (t), x_3,2 (t), and x_3,3 (t) by undergoing a transformation to obtain three signals u(t),v(t) and w(t) using the unit vectors V_3,1, V_3,2 and V_3,3. The one or more low frequency components comprises a low frequency signal u(t) that includes noise. Further, the one or more hardware processors are configured by the instructions to covert the low frequency signal u(t) to frequency domain by passing the low frequency signal u(t) through the Band-Pass Filter (BPF) and applying frequency domain transform like a Fourier Transform technique, wherein a frequency having the maximum power is estimated as the frequency of the Respiration Rate (RR), which is estimated ?RR?_in (i). Finally, the one or more hardware processors are configured by the instructions to perform a post-processing by invoking a retract module which reduces the fluctuation in the Respiration Rate (RR) estimates when the difference between the Respiration Rate (RR) estimate of any two successive windowed PPG signals > 2 breaths/min using an outline elimination technique, wherein the outline elimination technique uses a polynomial fit function.
In yet another aspect, there are provided one or more non-transitory machine-readable information storage mediums comprising one or more instructions, which when executed by one or more hardware processors causes a method for respiration rate estimation from PPG signal using an attractor reconstruction approach is provided. The processor-implemented method includes receiving, via an Input/Output (I/O) interface, a pre-defined raw Photoplethysmography (PPG) signal x_PPG (t) as input, wherein x_PPG (t) denotes a time series of a windowed PPG signal of a pre-defined duration. A delay value (t) is calculated for the received raw PPG signal x_PPG (t) to obtain a three-dimensional (3D) phase space signal x_3,1 (t), x_3,2 (t), x_3,3 (t) using a pre-defined delay technique and based on at least one of the below mathematical equations-
x_3,1 (t)= x_PPG (t); x_3,2 (t)=x_PPG (t- t) =x_3,1 (t- t); and x_3,3 (t)=x_PPG (t- 2t) =x_3,1 (t- 2t).
Further, one or more low frequency components are separated from one or more high frequency components of the signal x_3,1 (t), x_3,2 (t), and x_3,3 (t) by undergoing a transformation to obtain three signals u(t),v(t) and w(t) using the unit vectors V_3,1, V_3,2 and V_3,3, wherein the one or more low frequency components comprises a low frequency signal u(t) that includes noise. The low frequency signal u(t) is converted to frequency domain by passing the low frequency signal u(t) through the Band-Pass Filter (BPF) and applying frequency domain transform like a Fourier Transform technique, wherein a frequency having the maximum power is estimated as the frequency of the Respiration Rate (RR), which is estimated ?RR?_in (i). Finally, performing a post-processing by invoking a retract module which reduces the fluctuation in the Respiration Rate (RR) estimates when the difference between the Respiration Rate (RR) estimate of any two successive windowed PPG signals exceeds 2 BPM using an outline elimination technique, wherein the outline elimination technique uses a polynomial fit function.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, which are incorporated in and constitute a part of this disclosure, illustrate exemplary embodiments and, together with the description, serve to explain the disclosed principles:
FIG. 1 illustrates a block diagram of a system for respiration rate estimation from PPG signal using an attractor reconstruction approach, according to some embodiments of the present disclosure.
FIG. 2 is a flow chart to estimate the Respiratory Rate (RR) using the Attractor Reconstructor (AR) technique without discarding the vital signal, according to some embodiments of the present disclosure.
FIGS. 3A and 3B are exemplary flow diagrams to illustrate a processor-implemented method for respiration rate estimation from PPG signal using an attractor reconstruction approach, according to some embodiments of the present disclosure.
FIG. 4 is a schematic diagram of the PPG signal (32 second duration) acquired, according to some embodiments of the present disclosure.
FIG. 5A and 5B are block diagrams of RR estimation from attractor reconstruction (AR) technique, according to some embodiments of the present disclosure.
FIG. 6A through 6C are schematic diagrams to show three signals obtained using the delay of 1.6 second duration, according to some embodiments of the present disclosure.
FIG. 7 is a schematic diagram to show delay of 1.6 second duration to transform the PPG signal for estimating RR using AR technique, according to some embodiments of the present disclosure.
FIG. 8A through 8C are schematic diagrams to illustrate low frequency components from high frequency components, according to some embodiments of the present disclosure.
FIG. 9A and 9B are schematic diagrams to illustrate estimation of RR by filtering the u(t) using a band pass filter (BPF) and Fast Fourier Transform (FFT), according to some embodiments of the present disclosure.

DETAILED DESCRIPTION OF EMBODIMENTS
Exemplary embodiments are described with reference to the accompanying drawings. In the figures, the left-most digit(s) of a reference number identifies the figure in which the reference number first appears. Wherever convenient, the same reference numbers are used throughout the drawings to refer to the same or like parts. While examples and features of disclosed principles are described herein, modifications, adaptations, and other implementations are possible without departing from the scope of the disclosed embodiments.
Pervasive respiratory monitoring is a substantial need for an hour accommodated in lifestyle management, fitness programs, and the continuum of care. Photoplethysmography (PPG) is a non-invasive optical technique that can be used to detect blood volume changes in the microvascular bed of tissue. The PPG signal comprises two components: a pulsatile waveform (Alternating Current (AC)) attributed to changes in the interrogated blood volume with each heartbeat, and a slowly varying baseline (Direct current (DC)) combining low frequency fluctuations mainly due to respiration and sympathetic nervous system activity. Trend towards wearable device industry has made it easier for individuals to monitor their vital parameters at home using PPG signals, which provides valuable information to healthcare professionals. Thus, it’s clear that PPG has been widely accepted by the clinical community and research community, as a mean of non-invasive technique that is commonly used to measure RR.
Despite its non-invasive nature and ability to provide continuous monitoring, the PPG signal quality is a major concern. PPG signals are prone to various source of noise like inter-biological variation such as skin tone, obesity, age, and gender and intra-biological variability such as respiration, body temperature, site of measurement, and external factors such as motion artifact, pressure between sensor and the skin, and type of sensors. To overcome this, many research groups are working to extract the respiration signal and to estimate the RR from PPG, which can be categorized into three groups. The first category, extraction of the respiratory signal from PPG, is achieved by filtering the raw PPG signal. The second category, feature based techniques that extract the features like amplitude, width, height etc. from the signal. Third category is domain transformation like frequency domain such as Fourier transform, auto-regression, Welch method, joint time-frequency method. However, positive gradient based zero crossing is time domain-based estimation used for RR estimation.
Despite this fact, there exists a wide gap in standard preprocessing framework such as data recording duration, segmentation, filtering, and smoothing technique. In addition, the above techniques face the following limitations in RR estimation. a) Discarding the vital information to estimate the signal quality either manually or automatic SQI and discarding the windowed PPG to improve the accuracy of estimation. This feature parameter extraction depends on the user or expertise level, as they are manually curated parameters to get empirically hand-crafted features, and b) Need of external sensors to remove the noise in the PPG for respiration rate using additional sensors like accelerometer, pressure sensor.
Embodiments herein provide a method and system for Respiration Rate (RR) estimation from Photoplethysmogram (PPG) signal using an Attractor Reconstruction (AR) approach. The Attractor Reconstruction (AR) technique is used to extract respiratory signals and estimate the RR without discarding the vital signal. Herein, the naturally occurring baseline variation is separated by projecting the attractor onto a phase space using a delay coordinated from which new quantitative measures are obtained.
Further, there is an inclination towards multi-parameter estimation, explicitly focusing on the DC component of the PPG signal. At the same time, the AC component of the PPG signal relates to the heart. Precisely, the AC component reflects the change in blood volume due to the oscillation in blood cells and blood flow related to arterial blood pressure change. There are several ways to discriminate between these two components; one approach is AR. Ever since AR was first applied in the biological signal, it has been applied by various applications like Heart Rate (HR), Blood Pressure (BP), electroencephalogram (EEG) time series data. AR is also used for feature extraction, analyzing the signal morphology in a specific environment or a diseased state, and signal quality assessment. Thus, these advantages make AR-based techniques more suitable for human vital parameter estimation from wearable devices.
Referring now to the drawings, and more particularly to FIG. 1 through FIG. 9B, where similar reference characters denote corresponding features consistently throughout the figures, there are shown preferred embodiments, and these embodiments are described in the context of the following exemplary system and/or method.
FIG. 1 illustrates a block diagram of a system 100 for respiration rate estimation from Photoplethysmogram (PPG) signal using an attractor reconstruction approach, according to some embodiments of the present disclosure. Although the present disclosure is explained considering that the system 100 is implemented on a server, it may be understood that the system 100 may comprise one or more computing devices 102, such as a laptop computer, a desktop computer, a notebook, a workstation, a cloud-based computing environment and the like. It will be understood that the system 100 may be accessed through one or more input/output interfaces 104-1, 104-2... 104-N, collectively referred to as I/O interface 104. Examples of the I/O interface 104 may include, but are not limited to, a user interface, a portable computer, a personal digital assistant, a handheld device, a smartphone, a tablet computer, a workstation, and the like. The I/O interface 104 is communicatively coupled to the system 100 through a network 106.
One or more input hardware could be a wearable device, or the sensor device can be referred interchangeably in the disclosure. The wearable device is also configured to transmit the result of monitoring to a remote destination through wireless communication for medical assistance. The wearable device is adapted to acquire PPG using non-contact (in a partially or fully) sensing mechanism or in contact with optical sensing or piezo- electrical technique or diaphragm technique or video-based sensing. The wearable device is configured to monitor or determine the health and wellness of humans, in the real time.
In an embodiment, the network 106 may be a wireless or a wired network, or a combination thereof. In an example, the network 106 can be implemented as a computer network, as one of the different types of networks, such as virtual private network (VPN), intranet, local area network (LAN), wide area network (WAN), the internet, and such. The network 106 may either be a dedicated network or a shared network, which represents an association of the different types of networks that use a variety of protocols, for example, Hypertext Transfer Protocol (HTTP), Transmission Control Protocol/Internet Protocol (TCP/IP), and Wireless Application Protocol (WAP), to communicate with each other. Further, the network 106 may include a variety of network devices, including routers, bridges, servers, computing devices, storage devices. The network devices within the network 106 may interact with the system 100 through communication links.
The system 100 supports various connectivity options such as BLUETOOTH®, USB, ZigBee, and other cellular services. The network environment enables connection of various components of the system 100 using any communication link including Internet, WAN, MAN, and so on. In an exemplary embodiment, the system 100 is implemented to operate as a stand-alone device. In another embodiment, the system 100 may be implemented to work as a loosely coupled device to a smart computing environment. Further, the system 100 comprises at least one memory 110 with a plurality of instructions, one or more databases 112, and one or more hardware processors 108 which are communicatively coupled with the at least one memory to execute a plurality of modules 114 therein. The components and functionalities of the system 100 are described further in detail.
FIG. 2 is a flow chart 200 to outline the process of extracting the respiratory signal using the Attractor Reconstruction (AR) technique, according to some embodiments of the present disclosure. The AR technique facilitates evaluating the PPG signal, approximately periodic signals, by means of constructing a 3-dimensional (3D) attractor. The stages involved in transforming the PPG signal using AR technique is:
3D Signal Transformation - The 1-dimensional (1D) PPG signal (time series) is transformed to a three-dimensional (3D) attractor by means of Takens’ embedding theorem.
Baseline Elimination - It converts the 3D attractor to a two-dimensional (2D) attractor by splitting the signal into low frequency and high frequency components for estimating the vital parameters.
Density map - It projects the morphological changes of the PPG signal in each cycle, and it can be related to the behaviour of periodicity of a physiological signal. For instance, in the case of cardiovascular system say PPG or ECG, density map project the periodicity of PPG signals morphological variation due to medication or pathology or physiological conditions.
FIG. 3A and 3B (collectively referred as FIG. 3) is a flow diagram illustrating a processor-implemented method 300 for respiration rate estimation from Photoplethysmogram (PPG) signal using an attractor reconstruction approach implemented by the system 100 of FIG. 1. Functions of the components of the system 100 are now explained through steps of flow diagram in FIG. 3, according to some embodiments of the present disclosure.
Initially, at step 302 of the processor-implemented method 300, the one or more hardware processors 108 are configured by the programmed instructions to receive, via an input/output interface, a pre-defined raw Photoplethysmography (PPG) signal x_PPG (t) as input, wherein x_PPG (t) denotes a time series of a windowed PPG signal of a pre-defined duration. Let x_PPG(t) denote the time series of windowed PPG signal of desired duration (in sec) as shown in FIG. 4.
x_PPG (t)=(x_PPG,……..,x_na) (1)
where, ‘t’ is time in sec and ‘na' time duration of the signal in sec. The value of ‘a’ is 32, and by choosing ‘n’ as 1 or 2, the window size varies between 32 and 64.
FIG. 5A and 5B (collectively referred as FIG. 5) is a block diagram 500 to illustrate respiratory rate (RR) estimation from attractor reconstruction (AR) technique, according to some embodiments of the present disclosure. The RR estimation is done using the AR technique that generates three different PPG signals using the delay estimation.
At the next step 304 of the processor-implemented method 300, the one or more hardware processors 108 are configured by the programmed instructions to calculate a delay value (t) for the received raw PPG signal x_PPG (t) to obtain a three-dimensional (3D) phase space signal x_3,1 (t), x_3,2 (t), x_3,3 (t) as shown in FIG. 6A, 6B and 6C, using a pre-defined delay technique and based on at least one of the below mathematical equations:
x_3,1 (t)= x_PPG (t); (2)
x_3,2 (t)=x_PPG (t- t) =x_3,1 (t- t); (3)
x_3,3 (t)=x_PPG (t- 2t) =x_3,1 (t- 2t); (4)
x_(N,j) (t)=x_PPG (t-(j-1)t); (5)
where, N is the dimension for representing the signal (in this case (N = 3)) and j-varies from 1 to N. Thus, an attractor is reconstructed in a 3D phase space from a single signal, x_PPG (t), by using a vector of delay coordinates as given in equation (6).
x_3 (t)=??[ x?_3,1 (t),x_3,2 (t),x_3,3 (t)]?^T ?R^3 (6)
Selecting the delay value ‘t’, which is critical to generate an attractor with three-fold symmetry. However, for an approximate periodic signal, it has to be (1/3)rd of the length of one pulse wave or (1/3)rd of the average cycle length of the data as shown in FIG. 7. As an alternative approach the ‘t’ can be determined using various optimization techniques such as auto-correlation, L2 norm, entropy, etc.
At the next step 306 of the processor-implemented method 300, the one or more hardware processors 108 are configured by the programmed instructions to eliminate a baseline wander by generating a two new unit vectors V_3,2 and V_3,3 which are orthogonal with the unit vector (1,1,1), wherein the two new vectors V_3,2 and V_3,3 are generated along with V_3,1 such that these vector coordinates are orthogonal with each other.
Baseline Elimination: When the signal x_PPG (t) is varied by a constant C, then the derived signals are also varied by the same constant C.
x_(3,j) (t)=x_(3,j) (t)+C;where j=1,2,3 (7)
This overall shift in 3D phase space can be represented as x_3,1 (t),x_3,2 (t),x_3,3 (t)+C (1, 1, 1). This indicates that the 3D attractor points will also be shifted in the vector direction (1,1,1). This shift (C) is considered as noise or baseline wander that must be eliminated when processing the PPG signal. A line from the origin towards (1,1,1) is the central axis, and a unit vector in this direction is defined as in equation (8). In order to eliminate the noise or baseline wander, two new unit vectors are formed such that they are orthogonal with the unit vector (1,1,1). As a result, two new basis vectors V_3,2 and V_3,3 along with V_3,1 are generated, such that these vector coordinates are orthogonal with each other.
V_3,1= ?[1,1,1]?^T/v3= (1_(v3)^T)/v3 (8)
V_3,2= ?[1,-1,0]?^T/v2= ?[1,-1,? 0?_(N-2)]?^T/v2 (9)
V_3,3= ?[1,1,-2]?^T/v6= ?[1,1,-2,? 0?_(N-3)]?^T/v6 (10)
The equations (8), (9), and (10) can be generalized and represented as in equation (11), (12) respectively.
V_(N,1)= (1_N^T)/vN (11)
V_(N,M)= ?[1_(M-1),(M-1),0_(N-M)]?^T/v((M-1)^2+(M+1)) (12)
where, M > 1. The new coordinates (u, v, w) concerning the new basis vectors can be related to the old coordinates:
x_3 (t)=V_3 ?(t) (13)
?(t)=V_3^T x_3 (t) (14)
where, V_3 has columns V_3,1, V_3,2 and V_3,3 and ?(t) is [u(t),v(t),w(t)]^T. Further, the equation (13) and (14) can be elaborated as:
[¦(x_3,1 (t)@x_3,2 (t)@x_3,3 (t))]=[¦(1/v3&1/v2&1/v6@1/v3&(-1)/v2&1/v6@1/v3&0&(-2)/v6)][¦(u(t)@v(t)@w(t))] (15)

[¦(u(t)@v(t)@w(t))]=[¦(1/v3&1/v3&1/v3@1/v2&(-1)/v2&0@1/v6&1/v6&(-2)/v6)][¦(x_3,1 (t)@x_3,2 (t)@x_3,3 (t))] (16)

The equation (14) is represented as:
v(t)=V_3^T x_3 (t)+c[¦(1@1@1)] (17)

v(t)=V_3^T x_3 (t)+cV_3^T [¦(1@1@1)] (18)

Substituting equation (8) and (14) in equation (19):
?(t)=?(t)+v3 cV_3^T V_3,1 (19)
[¦(u(t)@v(t)@w(t))]=[¦(u(t)@v(t)@w(t))]+v3 c [¦(1/v3&1/v3&1/v3@1/v2&(-1)/v2&0@1/v6&1/v6&(-2)/v6)][¦(1/v3@1/v3@1/v3)] (20)

[¦(u(t)@v(t)@w(t))]=[¦(u(t)@v(t)@w(t))]+v3 c[¦(1@0@0)] (21)

u(t)=u(t)+v3 C;v(t); w(t)=w(t) (22)
It is evident from equation (22) that u(t) records baseline variation of the PPG signal and the other two variables v(t)and w(t) are invariant, such that it can be used to derive other information from the signal.
FIG. 8A through 8C (collectively referred as FIG. 8) are schematic diagrams to separate the low frequency components from high frequency components, the signal x_3,1 (t),x_3,2 (t),?and x?_3,3 (t) undergo a transformation to u(t), v(t), and w(t) using the vectors V_3,1, V_3,2 and V_3,3. It shows the transformed signals, u(t) shown in FIG. 8A, retains the low frequency signal like baseline variation, movement artifact, noise and so. Whereas v(t) and w(t), as shown in FIG. 8B and FIG. 8C respectively, retain the high periodic components. These periodic components are invariant to noise and can give a maximum three-fold symmetry. This resulted in 2D phase space having v(t), and w(t) and the density map of 2D attractor, which is used to estimate some of the vital parameters like HR.
At the next step 308 of the processor-implemented method 300, the one or more hardware processors 108 are configured by the programmed instructions to separate one or more low frequency components from one or more high frequency components of the signal x_3,1 (t), x_3,2 (t), and x_3,3 (t) by undergoing a transformation to obtain low frequency signals u(t),v(t) and w(t) using the unit vectors V_3,1, V_3,2 and V_3,3, wherein the one or more low frequency components comprises a low frequency signal u(t) that includes noise.
Density Map: Plotting the (v, w) plane signal results in line blurring with little detail, leading to inaccurate results. Hence, the projection of v(t) and w(t) plane into the density profile provides the variability of the waveform shape in each cycle. In the case of physiological signals, density maps provide the variation in heart rate or blood pressure, which would be a biomarker in the 2D attractor. As reported, ‘u(t)’ retains the low-frequency components, and the respiratory signal is a low-frequency component; herewith, we intend to extract the respiration signal and estimate the RR using the ‘u(t)’. In this work, the density map is out of scope.
At the next step 310 of the processor-implemented method 300, the one or more hardware processors 108 are configured by the programmed instructions to convert the low frequency signal u(t) to frequency domain by passing the low frequency signal u(t) via Band-Pass Filter (BPF) (U ^_PPG (t)) and applying a Fast Fourier Transform (FFT) technique as shown in FIG. 9A and 9B. Wherein, a frequency having the maximum power is estimated as the frequency of the Respiration Rate (RR), which is estimated ?RR?_in (i).
After extracting the ‘u(t)’, the estimation of RR consists of three steps: filtering, determining the dominant frequency, and re-tract module. The bandwidth of the ‘u(t)’ signal consists of noise, baseline drift, and other DC components, which affects their potential utility of parameter estimation. So, it is beneficial to filter the ‘u(t)’ signal prior to Fast Fourier Transform (FFT) or other frequency transformation technique for Respiration signal extraction, using a Band Pass Filter (BPF) with cut of frequency range of 0.1 - 0.5 Hertz, corresponding to the respiratory signal of human. Once the ‘u(t)’ signal is passed through the filter, e.g., FFT is applied, and the frequency having the maximum power is estimated as the frequency of the Respiration, which is determined as RRin(i). However, the accuracy of the dominant frequency is compromised due to the noise spectrum of the PPG signal, as average PSD decreases at the expense of frequency resolution. Hence, the Welch method is adapted in our work. Which effectively reduces the noise spectrum and improves the accuracy of RR estimation from the ‘u(t)’ signal.
Finally, at the last step 312 of the processor-implemented method 300, the one or more hardware processors 108 are configured by the programmed instructions to perform a post-processing by invoking a retract module which reduces the fluctuation in the Respiration Rate (RR) estimates when the difference between the Respiration Rate (RR) estimate of any two successive windowed PPG signals exceeds 2 breaths/min using an outline elimination technique. The outline elimination technique uses a polynomial fit (x ^[n]).
The re-tract module is invoked to reduce the fluctuation in the RR value when the difference between the RR estimate of any two successive windowed PPG signals exceeds 2 breaths/min. In this module, an ’outline elimination’ technique using a polynomial fit is applied as shown in equation (24).
?RR?_fin (i)={¦(if ?RR?_in (i)-?RR?_in (i-1)<2,@then ?RR?_fin (i)= ?RR?_in (i)@else ?RR?_fin (i)= ?0.8 ×RR?_in (i-1)+0.2×x ^[n])} (23)

x ^[n]=p[1]*x**(N)+p[2]*x**(N-1) (24)
wherein, the post-processing technique uses the coefficients (p[1] and p[2]) for a polynomial that is considered the best fit for the previous five RR estimates and calculates the final RR (RRfin) by a weighted sum of past RR estimate and the RR estimate obtained from the polynomial coefficients.
Decision block equation: The final RR (RRfin) is estimated for each window (i) till it reaches the maximum window count (W) of each dataset. The Window count is based on length of the signal (W=480 sec), window size (na) and step size (d =3). For all the windows, the RR is estimated and cross checked with the ground truth RR to check the correctness/accuracy of the estimation.

EXPERIMENTATION:
RR estimation: a) PSD (FFT & Welch) of band pass filtered PPG signal U ^_PPG (t)is compared with RRGT1; b) PSD (FFT & Welch) of U ^_PPG (t) is compared with RRGT2. The performance metric used for evaluation is the mean absolute error (MAE) as represented in equation (25):
MAE= 1/W ?_(i=1)^W¦?|RR_fin (i)-RR_true (i)|? (25)
where, W is the total number of windows used. The result indicates that the proposed method had an outcome by MAE of 1.53 BPM for a 64-sec windowed signal and 1.87 BPM for a 32-sec windowed signal. Even though the window size used for estimation is insignificant (MAE of 0.28 BPM), the result indicates that lower error rates are observed for 64-sec window size than 32-sec. To be more specific, in the small window of the duration of 32-sec, the AR reported an MAE of 2.59 BPM by FFT and 2.10 BPM by Welch for RRGT1 and 3.00 BPM by FFT and 2.64 BPM by Welch is reported for RRGT2. Similarly, for an increased window of 64-sec, MAE of 2.10 BPM by FFT and 1.82 BPM by Welch concerning RRGT1 and an error of 2.44 BPM by FFT and 2.19 BPM by Welch is reported to RRGT2. However, due to the reduced computation and processing time, there is always an inclination toward small, windowed signals, specifically for wearable devices. In contrast, a large window size may give accurate RR estimation at the expense of detection of the lowest RR.
The performance metric used for evaluation is compared with benchmark techniques shown in Table 1.
Dataset Algorithm MAE Window size
BIDMC Karlen [16] 5.80 32
Pimental [17] 4.00
Nilsson [14] 5.40
Fleming [11] 5.20
Iqbal [15] 3.97
Proposed 1 (FFT) 2.59
Proposed 2 (Welch) 2.10
Karlen [16] 5.70 64
Pimental [17] 2.70
Nilsson [14] 4.60
Fleming [11] 5.50
Iqbal [15] 3.35
Proposed 1 2.10
Proposed 2 1.82
Table 1
The written description describes the subject matter herein to enable any person skilled in the art to make and use the embodiments. The scope of the subject matter embodiments is defined by the claims and may include other modifications that occur to those skilled in the art. Such other modifications are intended to be within the scope of the claims if they have similar elements that do not differ from the literal language of the claims or if they include equivalent elements with insubstantial differences from the literal language of the claims.
The embodiments of present disclosure herein address unresolved problem of a) discarding the vital information wherein estimating the signal quality either manually or automatically using signal quality index (SQI) and discarding the windowed PPG to improve the accuracy of RR estimation b) need of external sensor to remove the noise in the PPG for RR using additional sensors like accelerometer, pressure sensor. Embodiments herein provide a method and system for Respiration Rate (RR) estimation from Photoplethysmogram (PPG) signal using an Attractor Reconstruction (AR) approach. The Attractor Reconstruction (AR) technique is used to extract respiratory signals and estimate the RR without discarding the vital signal. Herein, the naturally occurring baseline variation is separated by projecting the attractor onto a phase space using a delay coordinated from which new quantitative measures are obtained.
It is to be understood that the scope of the protection is extended to such a program and in addition to a computer-readable means having a message therein; such computer-readable storage means contain program-code means for implementation of one or more steps of the method, when the program runs on a server or mobile device or any suitable programmable device. The hardware device can be any kind of device which can be programmed including e.g., any kind of computer like a server or a personal computer, or the like, or any combination thereof. The device may also include means which could be e.g., hardware means like e.g., an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or a combination of hardware and software means, e.g., an ASIC and an FPGA, or at least one microprocessor and at least one memory with software processing components located therein. Thus, the means can include both hardware means, and software means. The method embodiments described herein could be implemented in hardware and software. The device may also include software means. Alternatively, the embodiments may be implemented on different hardware devices, e.g., using a plurality of CPUs.
The embodiments herein can comprise hardware and software elements. The embodiments that are implemented in software include but are not limited to, firmware, resident software, microcode, etc. The functions performed by various components described herein may be implemented in other components or combinations of other components. For the purposes of this description, a computer-usable or computer readable medium can be any apparatus that can comprise, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.
The illustrated steps are set out to explain the exemplary embodiments shown, and it should be anticipated that ongoing technological development will change the manner in which particular functions are performed. These examples are presented herein for purposes of illustration, and not limitation. Further, the boundaries of the functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternative boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed. Alternatives (including equivalents, extensions, variations, deviations, etc., of those described herein) will be apparent to persons skilled in the relevant art(s) based on the teachings contained herein. Such alternatives fall within the scope of the disclosed embodiments. Also, the words “comprising,” “having,” “containing,” and “including,” and other similar forms are intended to be equivalent in meaning and be open ended in that an item or items following any one of these words is not meant to be an exhaustive listing of such item or items or meant to be limited to only the listed item or items. It must also be noted that as used herein and in the appended claims, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise.
Furthermore, one or more computer-readable storage media may be utilized in implementing embodiments consistent with the present disclosure. A computer-readable storage medium refers to any type of physical memory on which information or data readable by a processor may be stored. Thus, a computer-readable storage medium may store instructions for execution by one or more processors, including instructions for causing the processor(s) to perform steps or stages consistent with the embodiments described herein. The term “computer-readable medium” should be understood to include tangible items and exclude carrier waves and transient signals, i.e., be non-transitory. Examples include random access memory (RAM), read-only memory (ROM), volatile memory, nonvolatile memory, hard drives, CD ROMs, DVDs, flash drives, disks, and any other known physical storage media.
It is intended that the disclosure and examples be considered as exemplary only, with a true scope of disclosed embodiments being indicated by the following claims.
, Claims:

A processor-implemented method (300) comprising:
receiving (302), via an Input/Output (I/O) interface, a pre-defined raw Photoplethysmography (PPG) signal x_PPG (t) as input, wherein x_PPG (t) denotes a time series of a windowed PPG signal of a pre-defined duration;
calculating (304), via one or more hardware processors, a delay value (t) for the received raw PPG signal x_PPG (t) to obtain a three-dimensional (3D) phase space signal x_3,1 (t), x_3,2 (t), x_3,3 (t) using a pre-defined delay technique and based on at least one of below mathematical equations:
x_3,1 (t)= x_PPG (t);
x_3,2 (t)=x_PPG (t- t) =x_3,1 (t- t);
x_3,3 (t)=x_PPG (t- 2t) =x_3,1 (t- 2t);
eliminating (306), via the one or more hardware processors, a baseline wander by generating at least two new unit vectors V_3,2 and V_3,3 which are orthogonal with a unit vector (1,1,1), wherein the at least two new vectors V_3,2 and V_3,3 are generated along with a vector V_3,1 such that coordinates of the vectors V_3,2, V_3,3 and V_3,1 are orthogonal with each other;
separating (308), via the one or more hardware processors, one or more low frequency components and one or more high frequency components of the three-dimensional (3D) phase space signal x_3,1 (t), x_3,2 (t), and x_3,3 (t) by undergoing a transformation to obtain signals u(t),v(t) and w(t) using the unit vectors V_3,1, V_3,2 and V_3,3, wherein a low frequency signal u(t) that includes noise comprises one or more low frequency components;
converting (310), via the one or more hardware processors, the low frequency signal u(t) to frequency domain by passing the low frequency signal u(t) through a Band-Pass Filter (BPF) and applying one or more frequency domain transformation techniques on the low frequency signal u(t), wherein a frequency having a maximum power is estimated as a frequency of respiration, which is estimated ?RR?_in (i); and
performing (312), via the one or more hardware processors, a post-processing by invoking a retract module which reduces fluctuation in the Respiration Rate (RR) estimates when the difference between the Respiration Rate (RR) estimates of any two successive windowed PPG signals exceeding two breath per minute (BPM) using an outline elimination technique, wherein the outline elimination technique uses a polynomial fit (x ^[n]).
The processor-implemented method (300) as claimed in claim 1, wherein the post-processing technique uses one or more polynomial coefficients and calculates a final Respiration Rate (?RR?_fin (i)) based on a weighted sum of past Respiration Rate (RR) estimates and one or more RR estimates obtained from one or more polynomial coefficients p[j].
?RR?_fin (i)={¦(if ?RR?_in (i)-?RR?_in (i-1)<2@then ?RR?_fin (i)=?RR?_in (i)@else ?RR?_fin (i)=0.8*?RR?_in (i-1)+0.2*x ^[n])¦
Where,x ^[n]= p[1]*x^N+p[2]*x^((N-1))
wherein N is the dimension for representing the PPG signal.
(i) represents total number of windows; and
polynomial coefficients p[1] and p[2] of the previous RR estimates.
The processor-implemented method (300) as claimed in claim 1, wherein a Welch technique is used to effectively reduce a noise spectrum and improve accuracy of Respiration Rate (RR) estimation from the low frequency signal u(t).

A system (100) comprising:
a memory (110) storing instructions;
one or more Input/Output (I/O) interfaces (104); and
one or more hardware processors (108) coupled to the memory (110) via the one or more I/O interfaces (104), wherein the one or more hardware processors (108) are configured by the instructions to:
receive, via an Input/Output (I/O) interface, a pre-defined raw Photoplethysmography (PPG) signal x_PPG (t) as input, wherein x_PPG (t) denotes a time series of a windowed PPG signal of a pre-defined duration;
calculate a delay value (t) for the received raw PPG signal x_PPG (t) to obtain a three-dimensional (3D) phase space signal x_3,1 (t), x_3,2 (t), x_3,3 (t) using a pre-defined delay technique and based on at least one of below mathematical equations-
x_3,1 (t)= x_PPG (t);
x_3,2 (t)=x_PPG (t- t) =x_3,1 (t- t);
x_3,3 (t)=x_PPG (t- 2t) =x_3,1 (t- 2t);
eliminate a baseline wander by generating at least two new unit vectors V_3,2 and V_3,3 which are orthogonal with a unit vector (1,1,1), wherein the at least two new vectors V_3,2 and V_3,3 are generated along with a vector V_3,1 such that coordinates of the vectors V_3,2, V_3,3 and V_3,1 are orthogonal with each other;
separate one or more low frequency components and one or more high frequency components of the three-dimensional (3D) phase space signal x_3,1 (t), x_3,2 (t), and x_3,3 (t) by undergoing a transformation to obtain signals u(t),v(t) and w(t) using the unit vectors V_3,1, V_3,2 and V_3,3, wherein a low frequency signal u(t) that includes noise comprises one or more low frequency components;
convert the low frequency signal u(t) to frequency domain by passing the low frequency signal u(t) through a Band-Pass Filter (BPF) and applying one or more frequency domain transformation techniques on the low frequency signal u(t), wherein a frequency having a maximum power is estimated as a frequency of respiration, which is estimated ?RR?_in (i); and
perform a post-processing by invoking a retract module which reduces fluctuation in the Respiration Rate (RR) estimates when the difference between the Respiration Rate (RR) estimates of any two successive windowed PPG signals exceeding two breath per minute (BPM) using an outline elimination technique, wherein the outline elimination technique uses a polynomial fit (x ^[n]).
The system (100) as claimed in claim 4, wherein the post-processing technique uses one or more polynomial coefficients and calculates a final Respiration Rate (?RR?_fin (i)) based on a weighted sum of past Respiration Rate (RR) estimates and one or more RR estimates obtained from one or more polynomial coefficients p[j].
?RR?_fin (i)={¦(if ? RR?_in (i)-?RR?_in (i-1)<2@then ?RR?_fin (i)=?RR?_in (i)@else ?RR?_fin (i)=0.8*?RR?_in (i-1)+0.2*x ^[n])¦
where,x ^[n]= p[1]*x^N+p[2]*x^((N-1))
wherein N is the dimension for representing the PPG signal;
(i) represents total number of windows; and
polynomial coefficients p[1] and p[2] of the previous RR estimates.

The system (100) as claimed in claim 4, wherein a Welch technique is used to effectively reduce a noise spectrum and improve accuracy of Respiration Rate (RR) estimation from the low frequency signal u(t).