Title: Non-Convex Weighted Lp Nuclear Norm based ADMM Framework for Image Restoration,
Abstract: Since the matrix formed by nonlocal similar patches in a natural image is of
low rank, the nuclear norm minimization (NNM) has been widely used in various
image processing studies. Nonetheless, nuclear norm based convex surrogate of
the rank function usually over-shrinks the rank components and makes different
components equally, and thus may produce a result far from the optimum. To
alleviate the above-mentioned limitations of the nuclear norm, in this paper we
propose a new method for image restoration via the non-convex weighted Lp
nuclear norm minimization (NCW-NNM), which is able to more accurately enforce
the image structural sparsity and self-similarity simultaneously. To make the
proposed model tractable and robust, the alternative direction multiplier
method (ADMM) is adopted to solve the associated non-convex minimization
problem. Experimental results on various types of image restoration problems,
including image deblurring, image inpainting and image compressive sensing (CS)
recovery, demonstrate that the proposed method outperforms many current
state-of-the-art methods in both the objective and the perceptual qualities.