Salt and pepper noise removal method based on stationary Framelet transform with non‐convex sparsity regularization

Salt and pepper noise occurs randomly and causes image degradation. Numerous denoising methods have been proposed to suppress this noise. However, existing methods have two main limitations. First, noise characteristics, such as noise location information and sparsity, are often described inaccurately or even ignored. Second, many existing methods separate the contaminated image into a recovered image and a noise part, leading to the recovery of an image with unsatisfactory smooth and detailed parts. In this study, the authors introduce a noise detection strategy to determine the position of the noise and employ a non‐convex sparsity regularization depicted byl p ${l_p}$ quasi‐norm to describe the sparsity of the noise, thereby addressing the first limitation. We adopt the morphological component analysis framework with stationary Framelet transform to decompose the processed image into the cartoon, texture, and noise parts to resolve the second limitation. Then, the proposed model is applied by using the alternating direction method of multipliers (ADMM). Finally, experiments are conducted to verify the proposed method and compare it with some current state‐of‐the‐art denoising methods. The experimental results show that the proposed method can remove salt and pepper noise while preserving the details of the processed image and outperforming some state‐of‐the‐art methods.