Block compressed sensing image reconstruction via deep learning with smoothed projected Landweber

Compressed sensing (CS) is a signal processing framework for effectively reconstructing signal from a small number of measurements obtained by linear projections of the signal. It is an ongoing challenge for the real-time image reconstruction of the computational imaging, including single pixel imaging based on CS. We built a block-based CS (BCS) image reconstruction framework via a deep learning network with smoothed projected Landweber (SPL). A fully connected network performs both BCS linear sensing and non-linear reconstruction stages, and SPL removes the blocking artifacts due to incorporate Wiener filtering into projected Landweber (PL) method at each iteration. The sensing matrix and nonlinear prediction operator are jointly optimized, and the smoothing filtering is coalesced into the PL framework for eliminating high-frequency oscillatory blocking artifact. Experimental results reveal that the optimized scheme outperforms the approach only based on deep neural network. The reconstruction quality can be improved while being only slightly slower, especially the gain of structural similarity is significantly better than peak signal-to-noise ratio, and the reconstruction image texture details are vivid and natural. At 10% sensing rate, the structural similarity maximum (minimum) gain reaches 0.098 (0.021). The proposed approach is not only far superior to other state-of-the-art CS algorithms in terms of reconstruction time and quality but also comparable with up-to-date deep learning methods.