DMFNet: deep matrix factorization network for image compressed sensing

Due to its outstanding performance in image processing, deep learning (DL) is successfully utilized in compressed sensing (CS) reconstruction. However, most existing DL-based reconstruction methods capture local features mainly through stacked convolutional layers while ignoring global structural information. In this paper, we propose a novel deep matrix factorization network (dubbed DMFNet), which takes advantage of detailed textures and global structural information of images to achieve better CS reconstruction. Specifically, the proposed DMFNet contains the sampling-initialization module and the DMF reconstruction module. In the sampling-initialization module, a saliency detector is employed to evaluate the salience of different regions and generate the corresponding feature map. Then, a block ratio allocation strategy (BRA) is developed to allocate CS ratios based on the feature map adaptively. Subsequently, we perform a block-by-block initialization reconstruction by a derived mathematical formula. In the DMF reconstruction module, we explore the global structural information by the low-rank matrix factorization. For the variable updating, we design the variables updating networks based on the deep unfolding networks (DUNs) and the U-net but not in a conventional way based on mathematical formulas. Extensive experimental results demonstrate that the proposed DMFNet obtains better reconstruction quality and noise robustness on several benchmark datasets compared to state-of-the-art methods.