Nonlocal low rank regularization method for fractal image coding under salt-and-pepper noise

Image denoising has been a fundamental problem in the field of image processing. In this paper, we tackle removing impulse noise by combining the fractal image coding and the nonlocal self-similarity priors to recover image. The model undergoes a two-stage process. In the first phase, the identification and labeling of pixels likely to be corrupted by salt-and-pepper noise are carried out. In the second phase, image denoising is performed by solving a constrained convex optimization problem that involves an objective functional composed of three terms: a data fidelity term to measure the similarity between the underlying and observed images, a regularization term to represent the low-rank property of a matrix formed by nonlocal patches of the underlying image, and a quadratic term to measure the closeness of the underlying image to a fractal image. To solve the resulting problem, a combination of proximity algorithms and the weighted singular value thresholding operator is utilized. The numerical results demonstrate an improvement in the structural similarity (SSIM) index and peak signal-to-noise ratio.