arXiv:1404.4774 [cs.CV]AbstractReferencesReviewsResources
Image Denoising with a Unified Schattern-$p$ Norm and $\ell_q$ Norm Regularization
Jing Wang, Meng Wang, Xuegang Hu, Shuicheng Yan
Published 2014-04-18, updated 2014-09-30Version 2
Image denoising is an important field in image processing since the common corruption in real world data. In this paper, we propose a non-convex formulation to recover the authentic structure from corrupted data. Typically, the specific structure is assumed to be low rank, which holds in a wide range of data, such as image and video. And the corruption is assumed to be sparse. In the literature, such problem is known as Robust Principle Component Analysis (RPCA), which usually recovers the low rank structure by approximating the rank function with a nuclear norm and penalizes the error by $\ell_1$-norm. Although RPCA is a convex formulation and can be solved effectively, the introduced norms are not tight approximations, which may deviate the solution from the authentic one. Therefore, we consider here a non-convex relaxation, consisting of a Schattern-$p$ norm and an $\ell_q$-norm that promote low rank and sparsity respectively. We derive a proximal iteratively reweighted algorithm (PIRA) to solve the problem. Our algorithm is based on alternating direction method of multipliers, where in each iteration we linearize the underlying objective function that allows us to have a closed form solution. We demonstrate that solutions produced by the linearized approximation always converge and have a tighter approximation than the convex counterpart. Experimental results on benchmarks show encouraging results of our approach.