RWRM: Residual Wasserstein regularization model for image restoration

Figure 11.  The curve graphs of parameter robustness. One can see that $ \lambda $ has a strong influence on PSNR in TV-L2 ($ \beta = 0 $), while in the RWRM ($ \beta \ne 0 $) PSNR is little affected by $ \lambda $. Thus, the parameters in our RWRM are robust

Figure 1.  Ten test images for Gaussian denoising. From left to right, they are Airfield, Lena, Peppers, Plane, Couple, Girl, Lake, Boat, Loco and Martha respectively

Figure 2.  TV-L2 denoising results on noisy image ($ \sigma = 25 $) with different regularization parameters $ \lambda $. One can find that the TV-L2 model with a moderate $ \lambda \in [1500,1800] $ can optimize the denoising effect

Figure 3.  Relationships between PSNR and model parameters taking the image "Boat". (a) In the TV-L2 model ($ \beta = 0 $), the effect of the parameter $ \lambda $ on PSNR. (b) In our RWRM, the effect of Wasserstein regularization parameter $ \beta $ on PSNR in the cases of three different $ \lambda $

Figure 4.  PSNR comparison curve on the ten images about the proposed RWRM ($ \beta \ne 0 $) and TV-L2 ($ \beta = 0 $) in Gaussian denoising

Figure 5.  The distribution comparison for the final residuals of TV-L2 (green), RWRM (red), and the ground truth (blue). One can see that RWRM residual estimate is more accurate than TV-L2

Figure 6.  Denoising results on the three images Peppers, Plane and Martha. Here (c) and (d) are the result images generated by the TV-L2 and our RWRM respectively. One can see that our approach clearly yields better visual results

Figure 7.  Local magnification comparison of denoised images. One can see that the RWRM can recover better image edge details

Figure 8.  Eight test images. From left to right, they are labeled as 1 to 8 respectively

Figure 9.  The denoising output results (PSNR and SSIM) of BM3D [5], NCSR [6], GHP [49] and our RWRM on the test image 8. From the first to the third row, the Gaussian noise standard deviations of the corresponding noisy images are 60, 80, and 100, respectively

Figure 10.  The denoising effect of RWRM and learning-based method LDCNN [48]

Figure 12.  Ten test images for non-blind deconvolution. From left to right, they are Plane, Glodhill, Couple, Peppers, Martha, Boat, Girl, Lena, Bacteria and Brain respectively

Figure 13.  The graph of the PSNR with $ \lambda $ in the RWRM ($ \beta = 0 $) applied to non-blind deconvolution

Figure 14.  The graph of the PSNR with $ \beta $ ($ \lambda = 1800 $) in the RWRM applied to non-blind deconvolution

Figure 15.  In non-blind deconvolution, PSNR comparison curves of the TV-L2 ($ \beta = 0 $) and the RWRM ($ \beta \ne 0 $) on the ten test images

Figure 16.  The results of non-blind deconvolution on the images Couple, Martha and Bacteria. Here (a) is the blurred and noisy images, (b) and (c) are the result images of the TV-L2 and the RWRM, respectively. One can see that the RWRM has obvious advantages in terms of both visual and numerical aspects

Figure 17.  Local enlarged images on non-blind deconvolution. One can see that the RWRM can recover better edge information

Figure 18.  Another eight test images for the non-blind deconvolution. From left to right, they are labeled as 1 to 8 respectively

Figure 19.  Visual effect comparison of non-blind deconvolution by three methods NL-$ {{\rm{H}}^{\rm{1}}} $, NL-TV and the proposed RWRM