Feature-Domain Proximal High-Dimensional Gradient Descent Network for Image Compressed Sensing

Compressed sensing theory can be used to solve the problem of limited computing resources of information source acquisition equipment, but there is uncertainty in the signal reconstruction process. Traditional reconstruction algorithm is difficult to be applied in practice because of its high computational complexity. Recently, the reconstruction algorithm based on deep learning has broken the limitation of traditional algorithms, and has attracted wide attention with its fast reconstruction speed and high quality. Existing deep learning reconstruction algorithms can be divided into two types: “black box” and optimization-based inspired network. Compared with the “black box” network structure, the optimization-inspired deep network is easier to obtain high-precision recovery and more interpretable. However, the existing image compressed sensing reconstruction optimization-inspired networks only learn a single gradient in each optimization phase and has shortcomings such as insufficient use of measured information and difficulty in learning gradients, limiting the improvement of reconstruction performance. In order to make full use of the measurement and reduce the difficulty of gradient learning, the idea of high-dimensional space gradient learning was proposed to achieve more accurate gradient regression. On this basis, this paper proposed Feature-domain Proximal High-Dimensional Gradient Descent (FPHGD) algorithm, and designed a Feature-domain Proximal High-dimensional Gradient Descent Network (FPHGD-Net) to realize this algorithm, so as to obtain high-precision image reconstruction. In addition, three kinds of deep space proximal mapping network structures with different complexity were designed to meet different application. According to the spatial complexity from low to high, the corresponding models are respectively called FPHGD-Net-Tiny, FPHGD-Net and FPHGDNet-Plus. Extensive experiment shows that, compared with OPINE-Net+, the average PSNR of the three proposed models on Set11 increase 1.34, 1.51 and 1.88 dB, and recover richer image details in the reconstruction of visual effects.