Reduction AWGN from Digital Images Using a New Local Optimal Low-Rank Approximation Method

In this paper, image noise reduction has been formulated as an optimization problem. The target image is denoised using a low-rank approximation of a matrix. Considering the fact that the smaller pieces of the picture are more similar (more dependent) in natural images, therefore, it is more logical to use low-rank approximation on smaller pieces of the image. In the proposed method, the image corrupted with additive white Gaussian noise (AWGN) is locally denoised, and the optimization problem of low-rank approximation is solved on all fixed-size patches (Windows with pixels needing to be processed). Therefore, for practical purposes, the proposed method can be implemented in parallel. This is one of the advantages of such methods. In all noise reduction methods, the two factors, namely the amount of the noise removed from the image and the preservation of the edges (vital details), are very important. In the proposed method, all the new ideas including the use of training image (TI image) obtained from the noisy image, the use of SVD adaptive basis, iterability of the algorithm, and patch labeling have all been proved to be efficient in producing sharper images, good edge preservation, and acceptable speed compared to the state-of-the-art denoising methods.