Recovering Texture with a Denoising-Process-Aware LMMSE Filter

Abstract

Image denoising methods generally remove not only noise but also fine-scale textures and thus degrade the subjective image quality. In this paper, we propose a method of recovering the texture component that is lost under a state-of-the-art denoising method called weighted nuclear norm minimization (WNNM). We recover the image texture with a linear minimum mean squared error estimator (LMMSE filter), which requires statistical information about the texture and noise. This requirement is the key problem preventing the application of the LMMSE filter for texture recovery because such information is not easily obtained. We propose a new method of estimating the necessary statistical information using Stein’s lemma and several assumptions and show that our estimated information is more accurate than the simple estimation in terms of the Fréchet distance. Experimental results show that our proposed method can improve the objective quality of denoised images. Moreover, we show that our proposed method can also improve the subjective quality when an additional parameter is chosen for the texture to be added.

Keywords

• image denoising
• image texture
• Stein’s lemma
• LMMSE filter
• low-rank approximation
• image processing