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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. [ABSTRACT FROM AUTHOR]

We propose the fractional-order total variation (TV) algorithm with nonlocal self-similarity for image reconstruction in compressed sensing to alleviate texture details deterioration and eliminate staircase artifacts, which results from the TV algorithms. The Grünwald–Letnikov fractional-order differential operators, which consider more neighboring image pixels and use four different directions to handle fractional-order gradients, are used to replace the integer-order differential operators. To suppress the staircase artifacts, modified nonlocal means operators are introduced into our method, which can contain prior image structural information and update the Lagrangian multipliers. An efficient augmented Lagrangian algorithm is used to solve the TV problem. Numerical results show that the algorithm achieves remarkable performance improvements at various sampling ratios. Compared with fractional-order TV-based projections onto convex sets, the maximum gains of peak signal-to-noise ratio and structural similarity index with all images are up to 2.52 dB and 0.0178, respectively, and the algorithm performs the better for preserving details and eliminating the staircase effect at the cost of taking more time. [ABSTRACT FROM AUTHOR]