IMAGE DENOISING VIA EXACT MINIMUM RANK APPROXIMATION WITH RELATIVE TOTAL VARIATION REGULARIZATION

Abstract

To 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 Schatten p-norm but also considered the prior knowledge where different rank components have different importance by relative total variation. Moreover, the alternating direction method of multipliers 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 evaluationthe proposed RTV-WSPM achieves significant improvements over the conventional WSPM under salt-and-pepper noise. Therefore, the RTV-WSPM exerts a good effect to restore the image structure and smoothness and improves denoising performances. Keywords: Weighted Schatten p-norm minimization; image denoising; low rank matrix approximation; RTV norm