Color images are described as digital data where 3-byte pixel values for the number of pixels are lined up in a series. Likewise, all types of digital data are described by a series of a finite number of symbols, and a binary digit (codeword) that is a combination of "0"and "1" is assigned to each symbol. The scheme of assigning the same length codeword regardless of symbols is called fixed-length coding. For example, in the series of symbols bcdaaaaaabaabbbdcbaa when 2-bit fixed length codes "00", "01", "10", "11"are assigned to "a", "b", "c", "d", the data volume (code volume) is equivalent to 40 bits. However, noting the occurrence of frequency of "a", then if different length codes are assigned as in Table 1.1, then the code volume will only be 24 bits. In this way short codewords are assigned to symbols with a high frequency of occurrence, and long codewords are assigned to symbols with a low frequency of occurrence and this scheme of compressing the code volume is referred to as variable-length coding or entropy coding. A classic example of variable-length coding is Huffman coding.                   Ultimately the picture quality of digital images is a subjective assessment based on human visual perception. Therefore the image does not need to be perfectly matched to the original image, and a reduction in brightness and color tone to some degree is acceptable for compression of the code volume. In particular, in the case of monochrome images, the process of reducing the grayscale (brightness) of the pixel values is called scalar quantization, and in the case of color images, the process of reducing the number of multiple pixel value set (RGB component) combinations is called Vector Quantization.     Example: Figure 1.2 shows the effect produced by reducing the code volume assigned for the pixel value of an 8-bit monochrome image in 2-bit stages. As the grayscale is reduced, distortions not present in the original image surface, and at 4 bits and under, a particular type of distortion referred to as false contours, results.                     Digital images come in a wide variety of forms including the binary images for facsimiles, natural images taken on digital cameras, and artificial images such as computer graphics and animation, etc. associated with games and amusement applications. All of these different types of digital images have different characteristics and properties. Therefore, direct entropy coding or scalar quantization alone cannot be expected to yield good results. As is shown in Fig. 1.3, the main method used involves performing an initial conversion (transformation) according to the nature of the digital image, and then converting the pixel value to a value with a higher occurrence of frequency, after which a decoding method that maximizes the effects of entropy coding is applied. lossy compression refers to encoding (compression) involving processes like quantization where data that should be present is lost, and lossless compression refers to the compression of images can be decoded (expanded) without any loss of the original data.