Improved RPCA method via non‐convex regularisation for image denoising

Abstract

The traditional robust principal component analysis (RPCA) model is based on the nuclear norm, which usually underestimates the singular values of the low‐rank matrix. As a consequence, the restoration image experiences serious interference by Gaussian noise, and the image quality degenerates during the denoising process. Therefore, an improved RPCA method via non‐convex regularisation terms is proposed to remedy the above shortcomings. First, in order to estimate the singular value of the low‐rank matrix more accurately, the authors employ the non‐convex penalty function and add a weight vector to it. Then, the regularisation with non‐convex penalty function and its weighted version are used to replace the nuclear norm and entry‐wise norm in original RPCA, respectively, to establish an improved model. Finally, an optimal solution algorithm is derived by developing the alternating direction multiplier method. Experimental results show that the proposed method has better performance in terms of both quantitative measurement and visual perception quality than other several state‐of‐the‐art image denoising methods.