A new image decomposition approach using pixel-wise analysis sparsity model

Decomposing an image into two ‘simpler’ layers has been widely used in low-level vision tasks, such as image recovery and enhancement. It is an ill-posed problem since the number of unknowns are larger than the input. In this paper, a two-step strategy is introduced, including task-aware priors estimate and a decomposition model. A pixel-wise analysis sparsity model is proposed to regularize the separation layers, which supposes the transformed image generated with analysis operator is sparse. Unlike regularizing all pixels with one penalty weight, we try to estimate each pixel’s sparsity level with task-aware priors and to achieve pixel-wise sparse penalty. Additionally, one separation layer is regularized with both synthesis sparsity model and pixel-wise analysis sparsity model to exploit their complementary mechanisms. Unlike the analysis one utilizing image local features, the synthesis one exploits an over-complete dictionary and non-local similarity cues to provide flexible prior for regularizing the decomposition results. The proposed model is solved by an alternating optimization algorithm. We evaluate it with two applications, Retinex model and rain streaks removal. Extensive experiments on multiple enhancement datasets, many synthetic and real rainy images demonstrate that our method can remove imaging noise during Retinex decomposition, and can produce high fidelity deraining results. It achieves competing performance in terms of quantitative metrics and visual quality compared with the state-of-the-art methods.