Plug-and-Play-Based Algorithm for Mixed Noise Removal with the Logarithm Norm Approximation Model

During imaging and transmission, images are easily affected by several factors, including sensors, camera motion, and transmission channels. In practice, images are commonly corrupted by a mixture of Gaussian and impulse noises, further complicating the denoising problem. Therefore, in this work, we propose a novel mixed noise removal model that combines a deterministic low-rankness prior and an implicit regularization scheme. In the optimization model, we apply the matrix logarithm norm approximation model to characterize the global low-rankness of the original image. We further adopt the plug-and-play (PnP) scheme to formulate an implicit regularizer by plugging an image denoiser, which is used to preserve image details. The above two building blocks are complementary to each other. The mixed noise removal algorithm is thus established. Within the framework of the PnP scheme, we address the proposed optimization model via the alternating directional method of multipliers (ADMM). Finally, we perform extensive experiments to demonstrate the effectiveness of the proposed algorithm. Correspondingly, the simulation results show that our algorithm can recover the global structure and detailed information of images well and achieves superior performance over competing methods in terms of quantitative evaluation and visual inspection.