Due to its great learning ability and fast processing speed, deep learning-based image compressive sensing (ICS) methods attract a lot of attention in recent years. However, the design of most existing ICS neural networks architecture ignore the mathematical theory in iterative optimization-based methods and cannot effectively use the prior structure knowledge in the signal, leading to lack of the interpretability. In order to retain the core ideas of the optimization algorithm and utilize the high performance of deep learning, this paper uses learnable convolutional layers to replace the predefined filters and artificial design parameters in the traditional smooth projected Landweber algorithm (SPL), and proposes a ICS neural network named SPLNet. In SPLNet, we design a unique network structure SPLBlock to implement three key steps in SPL iteration: (1) Wiener filter for removal of blocking artifacts; (2) approximation with projection onto the convex set; (3) bivariate shrinkage on transform domain for sparse representation and denoising. Experimental results indicate that, compared with current state-of-the-art ICS optimization iterative algorithm GSR, the average reconstructed image PSNR of SPLNet are improved by 0.78dB, and compared with state-of-the-art neural network framework SCSNet, the average reconstructed image PSNR of SPLNet are improved by 0.92dB.

The traditional iterative optimized based video compression sensing algorithms are limited by long running time and low adaptability of parameters,resulting in low practicability and generalization. Taking advantage of the powerful computing power, fast speed and learnable parameters of neural networks, this paper first proposes a group sparse representation network (VGSR-Net), which maps the image block group to a higher-dimensional sparse domain through convolution, and uses a learnable threshold to denoise and extract inter-frame correlation. On this basis, a two-stage recursive enhance reconstruction network (2sRER-VGSR-Net) is proposed. First, we perform VGSR-Net to preliminarily enhance the initial reconstruction and then introduce STMC-Net as motion estimation, and the compensated frames are fed into the residual reconstruction network to further extract the missing detail and enhance the current frame. The second stage of reconstruction adopts a hybrid recursive structure with the aim of making full use of the existing better quality reconstructed frames. The simulation results show that the proposed algorithm improves the PSNR (Reak Signal to Noise Ratio) by 1.99dB compared with the existing state-of-art traditional compressed video sensing reconstruction algorithms SSIM-InterF-GSR, while improves the PSNR by 4.60dB with the comparation of the network-based algorithm CSVideoNet.

Performance of dynamic sparse recovery for streaming signals in time domain will degrade for the existence of blocking artifacts and unknown time-varying noise intensity. To solve the above problems, a robust sparse Bayesian learning algorithm for dynamic compressive sensing of streaming signals in time domain is proposed based on the framework of lapped orthogonal transform and sparse Bayesian learning. In addition to eliminating the blocking artifacts, the proposed algorithm handles dynamic sparse Bayesian learning problems effectively under conditions of unknown time-varying noise intensity, which has better robustness against existing sparse Bayesian learning algorithms for streaming signals. Though there are not many existing effective algorithms for compressed sensing of streaming signals, experiments show that the proposed algorithm has obviously larger reconstruction signal-to-noise ratio and higher success rates for reconstruction than existing recovery algorithms for streaming signals based on sparse Bayesian learning or L1-homotopy; also, the measurement number required for particular success rates is obviously less than that of the other two algorithms, the computation cost and running time is approximately the same with the existing sparse Bayesian learning algorithm.

In order to improve the data reconstruction accuracy and alleviate the influence of packet loss over unreliable links on the Compressive Sensing (CS) data gathering in sensor networks, we propose a Packet Loss Matching Data Gathering Algorithm Based on Compressive Sensing (CS-MDGA) in this paper. This proposed algorithm establishes the correlation effect of the network data with the CS technique. We further design the Sparse Observation Matrix based on Packet Loss Matching (SPLM) in this paper. In addition, we prove that the designed observation matrix satisfies the Restricted Isometry Property (RIP) with a probability arbitrarily close to 1, which can guarantee the reliable delivery of the multi-path routing data among different nodes. The simulation results show that the relative reconstruction error of this proposed algorithm is still lower than 5% even when the packet loss rate of the link is as high as 60%. Therefore, it is verified that this proposed algorithm not only exhibits high reconstruction accuracy, but also effectively alleviates the influence of packet losses over unreliable links on the CS-based data collection.

Aiming at the difficulty of microwave imaging of strong scatterers, a multi-task Bayesian compressed sensing method based on Laplacian priori is proposed, which realizes microwave imaging of sparse strong scatterers. In the framework of contrast sources, sparse sensing model is established based on the "data" integral equation and the mesh discretization in the imaging region. The forward problem is simulated by the moment method; a Bayesian compressed sensing hierarchical model based on Laplacian priori is constructed; and in the case of multi-incident waves, multi-task Bayesian compressed sensing method is used to optimize the contrast source. Finally, the objective function is reconstructed by using the "state equation". Considering the influence of noise, Through the numerical simulation of multi-pixel single target, non-uniform single target and multi-target microwave imaging, and compared with the reconstructed results of conjugate gradient method and multi-task Bayesian compressed sensing method in the first-order Born approximation framework, which verifies the effectiveness and robustness of the proposed algorithm.