 block contains. If all of the coefficients are retained, the transformation can be reversed to arrive Fig. 3.8 DCT basis functions. Spatial, Temporal, and Statistical Redundancy coefficient 0 coefficients 0, 1, and 8 Fig. 3.9 Reconstructions of the Claire image. at the original pixels; in other words, the image has full fidelity. If, however, some of the coefficients are discarded and some of the frequency information is missing, degradations are introduced into the image reconstruction. This is shown in Figure 3.9, where the Claire test sequence has been transformed using the DCT and the image has then been reconstructed back into the pixel domain without using all the available coefficients. The figure on the left has been reconstructed using only coefficient 0 (i.e., the dc component), and the figure on the right uses coefficients 0, 1, and 8. Note there is an increase in fidelity when more coefficients are used and that if all 64 were used, the image would have full fidelity. Compression is generally achieved in DCT codecs by quantizing or leaving out some of the DCT coefficients. Two-Dimensional Variable-Length Coding Variable-length coding is used to code the DCT coefficients and is discussed later in this chapter. The result of applying the DCT transform to an 8 X 8 block of pixels is a block of 8 8 numbers or coefficients that represent the amount of each basis function (from Figure 3.8), which go to make up the block of pixels. Subjectively, the important information is generally contained in the top left of the figure, where the low-frequency components reside. Given that we wish to code this information, we can use variable-length coding but have the additional difficulty of needing to code a 2D array of numbers. To solve this, the 8 X 8 grid needs to be scanned. This is done in a zigzag fashion starting at the top left and descend- ing to the bottom right, as shown in Figure 3.10. This action produces an array of 64 coefficients. You will recall from Figure 3.7 that the eye is not very responsive to 