Weighted Norm Sparse Error Constraint Based ADMM for Image Denoising

In the process of image denoising, the accurate prior knowledge cannot be learned due to the influence of noise. Therefore, it is difficult to obtain better sparse coefficients. Based on this consideration, a weighted norm sparse error constraint (WPNSEC) model is proposed. Firstly, the suitable setting of power p in the norm is made a detailed analysis. Secondly, the proposed model is extended to color image denoising. Since the noise of RGB channels has different intensities, a weight matrix is introduced to measure the noise levels of different channels, and a multichannel weighted norm sparse error constraint algorithm is proposed. Thirdly, in order to ensure that the proposed algorithm is tractable, the multichannel WPNSEC model is converted into an equality constraint problem solved via alternating direction method of multipliers (ADMM) algorithm. Experimental results on gray image and color image datasets show that the proposed algorithms not only have higher peak signal-to-noise ratio (PSNR) and feature similarity index (FSIM) but also produce better visual quality than competing image denoising algorithms.