Tham khảo tài liệu 'a concise introduction to data compression- p4', công nghệ thông tin, cơ sở dữ liệu phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | The Discrete Cosine Transform 163 o Exercise Compute the one-dimensional DCT Equation of the eight correlated values 11 22 33 44 55 66 77 and 88. Show how to quantize them and compute their IDCT from Equation . The DCT in one dimension can be used to compress one-dimensional data such as a set of audio samples. This chapter however discusses image compression which is based on the two-dimensional correlation of pixels a pixel tends to resemble all its near neighbors not just those in its row . This is why practical image compression methods use the DCT in two dimensions. This version of the DCT is applied to small parts data blocks of the image. It is computed by applying the DCT in one dimension to each row of a data block then to each column of the result. Because of the special way the DCT in two dimensions is computed we say that it is separable in the two dimensions. Because it is applied to blocks of an image we term it a blocked transform. It is defined by n F2 Fm m 2y 1 - 2x 1 1 G V -nClC Pxycos 2m COS 2n x 0 y 0 L J L J for 0 i n 1 and 0 j m 1 and for Ci and Cj defined by Equation . The first coefficient Gqq is termed the DC coefficient and is large. The remaining coefficients which are much smaller are called the AC coefficients. The image is broken up into blocks of nx m pixels pxy with n m 8 typically and Equation is used to produce a block of n x m DCT coefficients Giy for each block of pixels. The top-left coefficient the DC is large and the AC coefficients become smaller as we move from the top-left to the bottom-right corner. The top row and the leftmost column contain the largest AC coefficient and the remaining coefficients are smaller. This behavior justifies the zigzag sequence illustrated by Figure . The coefficients are then quantized which results in lossy but highly efficient compression. The decoder reconstructs a block of quantized data values by computing the IDCT whose definition is pxy n 1 m 1 EE CiCjGij
