The Essential Guide to Image Processing- P13:We are in the middle of an exciting period of time in the field of image processing. Indeed, scarcely a week passes where we do not hear an announcement of some new technological breakthrough in the areas of digital computation and telecommunication. | Matrix-Vector Formulation 365 images after 20 iterations ISNR dB 50 iterations ISNR dB and at convergence after 330 iterations ISNR dB with the corresponding Hk u v in are shown respectively in Figs. a - c . In Fig. d the restored image ISNR dB by the direct implementation of the constrained least-squares filter in is shown along with the magnitude of the frequency response of the restoration filter. It is clear now by comparing the restoration filters of Figs. d and c and e and d that the high frequencies have been suppressed due to regularization that is the addition in the denominator of the filter of the term a C u v 2. Due to the iterative approximation of the constrained least-squares filter however the two filters shown in Figs. c and d differ primarily in the vicinity of the low-frequency zeros of D u v . Ringing is still present as it can be primarily seen in Figs. a and b although is not as visible in Figs. c and d . Due to regularization the results in Figs. c and d are preferred over the corresponding results with no regularization a shown in Figs. d and e . The value of the regularization parameter is very critical for the quality of the restored image. The restored images with three different values of the regularization a b FIGURE Continued 366 CHAPTER 15 Iterative Image Restoration FIGURE Restoration of the noisy-blurred image in Fig. a motion over 8 pixels BSNR 20dB a - c images restored by iteration after 20 iterations ISNR 50 iterations ISNR and at convergence after 330 iterations ISNR and the corresponding Hk w 0 in d image restored by the direct implementation of the constrained least-squares filter ISNR and the corresponding magnitude of the frequency response of the restoration filter Eq. . parameter are shown in Figs. a - c corresponding to a ISNR
