Wavelet frame based blind image inpainting

Split Bregman and Stationary Second-Degree Based Iterative Algorithm for Image Deconvolution

“…As for the algorithms in references [6] and [8], we employ their default settings. The experimental results are presented in Table 1 and Figures 2-3, where PSNR (peak signal-to-noise ratio) and MSE (mean square error) are defined as 10log 10 Table 1 and the images in Figure 2, we conclude that the presented algorithm can effectively restore common types of blurry images. Compared with similar deconvolution algorithms in experiment, the presented algorithm illustrates better performance.…”

“…To produce the blurry images shown in Figure 1 (c)-(f), the sharp images are first convolved by a Gaussian blur kernel and a uniform blur kernel, and then different levels of Gaussian noise are added to the blurry images. The Gaussian blur kernel and uniform blur kernel are generated using MATLAB functions fspecial('gaussian', [9 9], 9) and fspecial('average', [9 9]), respectively; the BSNR (blurred signal-to-noise ratio) is defined as 10log 10 [6] and [8] to restore the same blurry images. The algorithm in [6] uses an improved ITA to address the sparse representation based image deconvolution problem, and the algorithm in [8] uses Bregman iteration plus FBS to address the total variation based image deconvolution problem.…”

“…However, if the objective function of a minimization problem has more than one non-differentiable term, FBS cannot be applied to it. In addition to image deconvolution problems [8], FBS is also widely used to address some typical imaging inverse problems, such as image denoising [9], image inpainting [10] and so on. To solve problem P0 more efficiently, this paper presents a novel image deconvolution algorithm that is based on the split Bregman method (SBM) and the stationary seconddegree method (SSDM) [11].…”

Construction of Periodic Wavelet Frames Generated by the Walsh Polynomials

“…More precisely, they proved that under some decay conditions, the periodization of any wavelet frame constructed by the unitary extension principle is a periodic wavelet frame, and the periodization of any pair of dual wavelet frames constructed by the mixed extension principle is a pair of dual periodic wavelet frames. To mention only a few references on wavelet frames, the reader is referred to [5][6][7][8] and the many references therein.…”

Mixed Noise Removal by Weighted Encoding With Sparse Nonlocal Regularization

“…This method achieves competitive mixed noise removal results but with much better computational performance. Dong et al [35] presented two sparsity-based regularization models for blind inpainting problems. A new variable is introduced in the data fidelity term to represent the outliers.…”