A Dictionary-learning-based Denoising Algorithm with log-regularizer for MR Image

摘要

With the wide application of magnetic resonance imaging (MRI) technology in the medical field, MR image denoising draws a lot of research attention. The dictionary learning methods based on sparsity representation analysis models have been developed for image denoising recently. Despite these methods solve a class of challenging nonconvex and nonsmooth, it remains an hot topic to find a dictionary learning method that is not only empirically fast, but also has mathematically guaranteed strong convergence. In this paper, we employ log-regularizer instead of ℓ₀ norm and ℓ₁ norm sparsity regularizer, and than we propose a novel dictionary-learning-based denoising algorithm with log-regularizer for MR image. To solve the optimization problem efficiently, we divide MR image into local image patches. And then, we decompose the overall problem in matrix form into subproblems in vector form. In the final, we adopt alternating optimization scheme to update sparse vectors, dictionary atoms and the reconstructed MR image alternately. In addition, proximal operator algorithm and the least square method are employed to obtain the solutions of sparse vectors and dictionary atoms, leading to an efficient and fast algorithm. More importantly, a theoretical analysis shows the proposed algorithm satisfies the global convergence property. Experiments also show that the proposed algorithm achieves better results compared with other dictionary-learning-based denoising algorithms.