Many analysis-based regularizations proposed so far employ a common prior information, i.e., edges in an image are sparse. However, in local edge regions and texture regions, this prior may not hold. As a result, the performance of regularizations based on the edge sparsity may be unsatisfactory in such regions for image-related inverse problems. These regularizations tend to smooth out the edges while eliminating the noise. In other words, these regularizations' abilities of preserving edges are limited. In this paper, a new prior that the corner points in a natural image are sparse was proposed to construct regularizations. Intuitively, even in local edge regions and texture regions, the sparsity of corner points may still exist, and hence, the regularizations based on it can achieve better performance than those based on the edge sparsity. As an example, by utilizing the sparsity of corner points, we proposed a new regularization based on Noble's corner measure function. Our experiments demonstrated the excellent performance of the proposed regularization for both image denoising and deblurring problems, especially in local edge regions and texture regions.
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