Figure 6.4 shows the same image reproduced by inverse DCT of the lower DCT coefficients. This image is the pseudo-inverse spectral solution (5.11) and has negative values and values greater than 1, so is not a valid image.
Figure 6.5 shows the MaxEnt solution , to maximizing (6.6) subject to (5.12). Like the image in Figure 6.4, it is feature reproducing, but has values in . Note the better image characteristics at edges and lines. See software/image_ex2.m.
For comparison purposes, we re-ran the maximization using the positive assumption of section 5, obtaining the solution to the maximization of (5.14) subject to (5.12). This is essentially a maximum entropy 2-D spectrum because the 2-D DCT of the image can be considered the auto-correlation function. It is the formulation used by a significant amount of the literature in image reconstruction . Figure 6.6 shows the resulting image. Although still showing improvement in sharpness over Figure 6.4, we see immediately the effect of having no upper bound on the pixel intensity and increased Gibbs-effect. The result is less pleasing to the eye than Figure 6.5.