Low-Rank Estimation for Image Denoising Using Fractional-Order Gradient-Based Similarity Measure

Abstract

The aim of this paper is to introduce a novel similarity measure using fractional-order derivative for patch comparison in low-rank image denoising approach. Recently, several outstanding low-rank image denoising algorithms have been proposed. However, these methods have limitations in the sense that certain irrelevant patches can be selected during patch comparison. These undesired patches affect singular values shrinkage and aggregation phases of these approaches. Thus, the fine details and edges of denoised image may not be well preserved. To address this issue, a novel method is proposed in which gradient information is injected in patch comparison using discretized fractional-order derivatives. The advantages of proposed approach are twofold: firstly, the patch comparison becomes more reliable by combining intensity and gradient information; secondly, the fractional-order gradient provides an additional degree of freedom to quantify the gradient information for patch comparison in an efficient way. In addition, the proposed algorithm estimates noise level using geometric details encoded in the image patches. The noise estimation strategy may help in terminating the iterative low-rank approximation. Experimental results on test images reveal that the proposed method performs better than several outstanding algorithms, specifically, in the presence of severe noise levels.