Multi-scale Fractional-Order Sparse Representation for Image Denoising

Sparse representation models code image patches as a linear combination of a few atoms selected from a given dictionary. Sparse representation-based image denoising (SRID) models, learning an adaptive dictionary directly from the noisy image itself, has shown promising results for image denoising. However, due to the noise of the observed image, these conventional models cannot obtain good estimations of sparse coefficients and the dictionary. To improve the performance of SRID models, we propose a multi-scale fractional-order sparse representation (MFSR) model for image denoising. Firstly, a novel sample space is re-estimated by respectively correcting singular values with the non-linear fractional-order technique in wavelet domain. Then, the denoised image can be reconstructed with the accurate sparse coefficients and optimal dictionary in the novel sample space. Compared with the conventional SRID models and other state-of-the-art image denoising algorithms, the experimental results show that the performances of our proposed MFSR model are much better in terms of the accuracy, efficiency and robustness.