Gaussian Blur with Additive Gaussian Noise. Next, we add 1% Gaussian noise to the Gaussian blurred image and deblur it with different boundary conditions. The noisy blurred image is shown Reflective BC Periodic BC Zero BC deblurred image zoom: table zoom: face Synthetic BC Anti-reflective BC Figure 2.9: Deblurring results on motion blurred “Xxxxxxx” with different boundary conditions blurred image zoom: table zoom: face in Figure 2.10 and the deblurring results are shown in Figure 2.11. The corresponding PSNRs are shown in Table 2.3, and the relative error plot against iteration is shown in Figure 2.12(a). In this case, anti-reflective boundary conditions give the best result, re- flective boundary conditions the second best, and synthetic boundary condi- tions a close third. One may suggest that in the process of obtaining synthetic boundary conditions from the noisy image, noise is taken as image feature and incorrect boundary conditions are obtained. However, we believe this is not true; we applied the synthetic boundary conditions, obtained from the noisy blurred image, to deblur the corresponding noise-free blurred image, and obtained the very good results shown in Figure 2.13, with a PSNR of 28.5262dB. This illustrates that good synthetic boundary conditions can still be obtained from noisy images. In fact, except for some pixels near the boundary, it is difficult to de- Reflective BC Periodic BC Zero BC deblurred image zoom: table zoom: face Synthetic BC Anti-reflective BC Figure 2.11: Deblurring results on noisy Gaussian blurred “Xxxxxxx” with different boundary conditions
(a) whole image (b) outermost 5 pixels excluded Figure 2.12: Plot of the deblurring errors vs iteration on noisy Gaussian blurred image. deblurred image zoom: table zoom: face Figure 2.13: Deblurring result of Gaussian blurred “Xxxxxxx” with the syn- thetic boundary conditions obtained from the blurred and noisy counterpart. Its PSNR to the original image is 28.5dB. termine visually if synthetic boundary conditions really perform worse than reflective and anti-reflective boundary conditions. Note that if we exclude the outermost 5 pixels in the calculation of relative errors and PSNRs, anti- reflective and synthetic boundary conditions give very similar results (cf. Fig- ure 2.12(b) and Table 2.4), with slightly better results being obtained with synthetic boundary conditions.
