Reciprocal transformation based convex variational image restoration with multiplicative noise
Yu Gan, Zhifang Liu, Huibin Chang · Inverse Problems and Imaging · 2024
Image restoration with multiplicative noise is widely studied in image processing, among which how to overcome the non-convexity of the model is of vital importance. By introducing a reciprocal transformation related to the image variable in the model proposed by Aubert and Aujol (AA) and approximating the total variation term, the reciprocal transformation based convex denoising (RTC) model and the weighted RTC (wRTC) model are proposed for multiplicative noise removal. To handle blurry images, we further introduce a constraint related to the blur operator, resulting in the reciprocal transformation based convex restoration (RTCr) model. To solve these proposed models efficiently, the primal-dual algorithm and the proximal alternating linearized minimization method are utilized. Numerical experiments demonstrate that the proposed methods produce good restoration results in terms of SNRs/computational efficiency compared with some typical variational methods for multiplicative noise removal.