Image denoising via exact minimum rank approximation with relative total variation regularization

Abstract

Image denoising is one of the classical problems in image

processing. Such denoising by minimum rank approximation via

Schatten p-norm minimization is prone to cause over-smoothing.

Intricate and irregular image structures cann’t be distinguished

dramatically by Schatten p-norm minimization. A flexible and

precise model named weighted Schatten p-norm minimization

(WSPM) with relative total variation regularization (RTV-WSPM)

was proposed in this study to address this issue. The proposed

RTV-WSPM not only had an accurate approximation with a Schat

ten p-norm but also considered the prior knowledge where differ

ent rank components have different importance by relative total

variation. Moreover, the alternating direction method of multi

pliers was introduced to solve the proposed RTV-WSPM model.

Experiments on Gaussian white noise and salt-and-pepper noise

demonstrate that the proposed technique outperforms other

state-of-the-art methods, especially under degradation for high

density image noise. In terms of peak signal-to-noise ratio evalu

ationthe proposed RTV-WSPM achieves significant improvements

over the conventional WSPM under salt-and-pepper noise. There

fore, the RTV-WSPM exerts a good effect to restore the image

structure and smoothness and improves denoising performances