Image Denoising via Nonlocally Sparse Coding and Tensor Decomposition

The nonlocally sparse coding and collaborative filtering techniques have been proved very effective in image denoising, which yielded state-of-the-art performance at this time. In this paper, the two approaches are adaptively embedded into a Bayesian framework to perform denoising based on split Bregman iteration. In the proposed framework, a noise-free structure part of the latent image and a refined observation with less noise than the original observation are mixed as constraints to finely remove noise iteration by iteration. To reconstruct the structure part, we utilize the sparse coding method based on the proposed nonlocally orthogonal matching pursuit algorithm (NLOMP), which can improve the robustness and accuracy of sparse coding in present of noise. To get the refined observation, the collaborative filtering method are used based on Tucker tensor decomposition, which can takes full advantage of the multilinear data analysis. Experiments illustrate that the proposed denoising algorithm achieves highly competitive performance to the leading algorithms such as BM3D and NCSR.