TABLE OF CONTENTS Exactly as in 1-D, redundancy has many advantages, that more than compensate the higher computational cost it implies. In a nutshell, redundant decompositions lead to better quality reconstructions and are more robust to noise. Actually, the whole discussion of Section 1.6.2 could be repeated here almost verbatim, in particular concerning the robustness issue.
We highlight the reconstruction aspect with one striking example. We consider the standard barbara image and decompose it in two ways, first with an orthonormal wavelet basis (using 2-D Daubechies DB4 wavelets), then with a redundant frame of directional wavelets. The images reconstructed by the two methods are presented in Figure 2.14. Panels (a) and (b) show the reconstruction using 3 bits per coefficient, while (c) and (d) show the result obtained with 2 bits per coefficient. In either case, the resulting image is visually better when the redundant frame is used, (b) or (d). The orthonormal basis gives more artifacts and distortions. Of course, the effect is more marked in the 2 bit case. Although the two results are poor, we show them for emphasizing the point.
