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Biomedical Signal and Image Processing
Yc=zeros(256,256);

Yc(1:128, 1:128)=Y(1:128, 1:128);

Xc=idct2(Yc);

figure;

colormap(gray(256) );

image(Xc);

As can be seen, only a small number of DCT coefficients located in the top left
corner of the DCT domain (i.e., the low frequency coefficients with small u and
v indices) are significant and the rest of the coefficients are very close to 0. This
means that if we keep only the significant coefficients (e.g., the coefficients whose
absolute values is larger than a threshold value), the only coefficients that will survive are the ones in the top left corner. As shown in Figure 6.1c, reconstruction of
the image using only the coefficients in the top left quadrant of the DCT domain
results to a high-quality approximation of the image. In other words, using only a
quarter of the original DCT coefficients will allow producing a high-quality reconstruction of the original image. This compression process is the principal idea of
some practical systems such as the older versions of the JPEG technology.
FIGURE 6.1 (a) Original image, (b) DCT of the image, and (c) reconstructed image using
only the coefficients in the top left quadrant of the DCT domain. (From Goldberger, A.L.
et al., Circulation, 101(23), e215, 2000, Circulation Electronic Pages; http://circ.ahajournals.
org/cgi/content/full/101/23/e215).