Transformer based Douglas-Rachford unrolling network for compressed sensing

Compressed sensing (CS) with the binary sampling matrix is hardware-friendly and memory-saving in the signal processing field. Existing Convolutional Neural Network (CNN)-based CS methods show potential restrictions in exploiting non-local similarity and lack interpretability. In parallel, the emerging Transformer architecture performs well in modelling long-range correlations. To further improve the CS reconstruction quality from highly under-sampled CS measurements, a Transformer based deep unrolling reconstruction network abbreviated as DR-TransNet is proposed, whose design is inspired by the traditional iterative Douglas-Rachford algorithm. It combines the merits of structure insights of optimization-based methods and the speed of the network-based ones. Therein, a U-type Transformer based proximal sub-network is elaborated to reconstruct images in the wavelet domain and the spatial domain as an auxiliary mode, which aims to explore local informative details and global long-term interaction of the images. Specially, a flexible single model is trained to address the CS reconstruction with different binary CS sampling ratios. Compared with the state-of-the-art CS reconstruction methods with the binary sampling matrix, the proposed method can achieve appealing improvements in terms of Peak Signal to Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM) and visual metrics. Codes are available at https://github.com/svyueming/DR-TransNet.