Estimation of the parameters of a weighted nuclear norm model and its application in image denoising

Abstract

In this study, a method for optimizing a weighted nuclear norm model is proposed. This model optimization solution employs a soft-thresholding operation on the singular values of an observation matrix. To determine the soft-thresholding, we focused on the unique properties of a class of special matrices, termed rank-order similar matrices (ROSMs). The threshold determination problem was solved during training by exploiting these properties. In addition, we applied this optimization method to image denoising. In this application, the denoising does not work on the whole image at once, but rather relies on a set of ROSMs. Each matrix in the set is an ROSM, built by stacking non-local similar patch vectors. This optimization method is applied to every ROSM in the set to obtain estimates of the underlying patches, which are aggregated to reconstruct a restored image. Simulation results of 154 noisy images indicate that the proposed optimization method achieves the same peak signal to noise ratio/mean structural similarity index measure results as those achieved by several other state-of-the-art methods such as block-matching and 3D filtering and weighted nuclear norm minimization. It also outperforms many state-of-the-art methods such as nuclear norm minimization, in terms of the visual quality of images.