Synthesis-analysis deconvolutional network for compressed sensing

Synthesis learning and analysis learning, with sparse coding (SC) and Markov random fields (MRFs) as two representative types of models, are two complementary tools to describe the image manifolds. SC has strengths in representing the regular features/explicit visual manifolds while its effectiveness depends on the training dataset. While MRFs have great potentials to characterize the stochastic textures/implicit visual manifolds but at the cost of high training complexity. In this paper, by means of the convolutional operator, a unified synthesis and analysis deconvolutional network (SADN) is presented. It not only requires the generative coding coefficients to be sparse, but also enforces the convolution between the filter and trained images to be sparse. The proposed model incorporates the strengths of both SC and MRFs, which enables it to represent general images with both generative and discriminative abilities. The resulting minimization is tackled by the combination of alternating optimization and Iterative Re-weighted Least Square (IRLS). Experiments conducted on compressed sensing (CS) application show its great potentials both quantitatively and qualitatively.