Hybrid model of tensor sparse representation and total variation regularization for image denoising

The method based on non-local self-similarity patches has been widely applied in image denoising. For a given image patch, there are similar image patches at neighbor windows in the image. Traditionally, similar patches are vectorized and then rearranged into a matrix, which should have a low rank. Hence the denoising problem can be reformulated into a low rank recovery problem. However, the vectorization process can disrupt the spatial relationships among the patches. To improve this drawback, we rearrange the similar patches into a tensor to keep the spatial relationships. When the higher-order singular value decomposition (HOSVD) is applied to this tensor, the resulting core tensor should be sparse. In this paper, the sparse property of the core tensor is utilized to characterize similar patches, and then an optimization model is derived. Since the commonly used l0 norm regularization is NP-hard, we adopt the MCP function to constrain the sparse property of the core tensor. In addition, a total variation (TV) regularization term for the tensor is added to the model to preserve structural information in the image such as edges. Using the dual form to represent the total variation regularization and transforming the original problem into a saddle point problem, the primal–dual algorithm is applied to overcome the non-differentiability of the TV regularization. Finally, experimental results demonstrate that compared to existing denoising methods, the method proposed can better preserve details and structural information in the image.