1. An image encoding device comprising:
an image compressor that carries out a transformation process on a difference image between an image and a prediction image, quantizes transform coefficients of the difference image, and outputs the quantized transform coefficients as compressed data;
a filter that carries out a filtering process on a decoded image which is a result of addition of the difference image decoded from the compressed data and the prediction image; and
an encoder that encodes the compressed data and a filter parameter used when the filtering process is carried out by the filter and generates a bitstream,
wherein the filter determines a classification method of a class on each coding block having a largest size, carries out a classification on each pixel within each coding block having the largest size by using the classification method, calculates an offset value for each class for each coding block having the largest size, and carries out a pixel adaptive offset process by which the offset value is added to a pixel value of a pixel belonging to a corresponding cl-ass, and
the encoder encodes a quantization matrix parameter for generating a quantization matrix used when the transform coefficients are quantized by the image compressor and an index indicating the classification method of a class on each coding block having the largest size, the classification method being determined by the filter, and encodes a parameter of the offset value for each class on a basis of a binarization process using a truncated unary code, the offset value being determined on a basis of a pixel value of pixels adjacent to a pixel to which the offset value is added, and
a maximum of the offset value is determined by a bit depth of the decoded image.

2. An image decoding device comprising:
a decoder that decodes compressed data, a filter parameter and a quantization matrix parameter from coded data multiplexed into a bitstream;
a difference image generator that inverse-quantizes transform coefficients obtained from the compressed data by using the quantization matrix parameter which is decoded by the decoder and inverse-transforms the inverse-quantized transform coefficients to generate a difference image;
a decoded image generator that adds the difference image and a prediction image to generate a decoded image; and
a filter that carries out a filtering process on the decoded image decoded from the compressed data by using the filter parameter,
wherein the decoder decodes, as a filter parameter, an index indicating a classification method of a class on each coding block having a largest size from the coded data, and decodes a parameter of an offset value for each class on which a binarization process using a truncated unary code is performed, the offset value being determined on a basis of a pixel value of pixels adjacent to a pixel to which the offset value is added,
the filter specifies the classification method of a class on each coding block having the largest size by using the index, carries out a classification on each pixel by using the classification method, and carries out a pixel adaptive offset process by which the offset value is added to a pixel value of a pixel belonging to a corresponding class, and
a maximum of the offset value is determined by a bit depth of the decoded image.