Using Marchenko–Pastur SVD and Linear MMSE Estimation for Reducing Image Noise

The degradation in visual quality of images is often seen due to a variety of noise added inevitably at the time of image acquisition. Its restoration has thus become a fundamental and significant problem in image processing. Many attempts are made in recent past to efficiently denoise images. But, the best possible solution to this problem is still an open research problem. This paper validates the effectiveness of one such popular image denoising approach, where an adaptive image patch clustering is followed by the two step denoising algorithm in Principal Component Analysis (PCA) domain. First step uses Marchenko–Pastur law based hard thresholding of singular values in the singular value decomposition (SVD) domain and the second step removes remaining noise in PCA domain using Linear Minimum Mean-Squared-Error (LMMSE), a soft thresholding. The experimentation is conducted on gray-scale images corrupted by four different noise types namely speckle, salt & pepper, Gaussian, and Poisson. The efficiency of image denoising is quantified in terms of popular image quality metrics peak signal-to-noise ratio (PSNR), structural similarity (SSIM), feature similarity (FSIM), and the denoising time. The comprehensive performance analysis of the denoising approach against the four noise models underlies its suitability to various applications. This certainly gives the new researchers a direction for selection of image denoising method.