Non-Convex Low-Rank Approximation for Image Denoising and Deblurring

Recovery of low-rank matrices has seen significant activity in many areas of science and engineering, motivated by theoretical results for exact reconstruction guarantees and interesting practical applications. Recently, numerous methods incorporated the nuclear norm to pursue the convexity of the optimization. However, this greatly restricts its capability and flexibility in dealing with many practical problems, where the singular values have clear physical meanings. This paper studies a generalized non-convex low-rank approximation, where the singular values are in l(p)-heuristic. Then specific results are derived for image restoration, including denoising and deblurring. Extensive experimental results on natural images demonstrate the improvement of the proposed method over the recent image restoration methods.