Image Compressed Sensing using Convolutional Neural Network.

In the study of compressed sensing (CS), the two main challenges are the design of sampling matrix and the development of reconstruction method. On the one hand, the usually used random sampling matrices (e.g. GRM) are signal independent, which ignore the characteristics of the signal. On the other hand, the state-of-the-art image CS methods (e.g. GSR and MH) achieve quite good performance, however with much higher computational complexity. To deal with the two challenges, we propose an image CS framework using convolutional neural network (dubbed CSNet) that includes a sampling network and a reconstruction network, which are optimized jointly. The sampling network adaptively learns the sampling matrix from the training images, which makes the CS measurements retain more image structural information for better reconstruction. Specifically, three types of sampling matrices are learned, i.e. floating-point matrix, {0,1}-binary matrix, and {-1,+1}-bipolar matrix. The last two matrices are specially designed for easy storage and hardware implementation. The reconstruction network, which contains a linear initial reconstruction network and a non-linear deep reconstruction network, learns an end-to-end mapping between the CS measurements and the reconstructed images. Experimental results demonstrate that CSNet offers state-of-the-art reconstruction quality, while achieving fast running speed. In addition, CSNet with {0,1}-binary matrix, and {-1,+1}-bipolar matrix gets comparable performance with the existing deep learning based CS methods, and outperforms the traditional CS methods. What's more, the experimental results further suggest that the learned sampling matrices can improve the traditional image CS reconstruction methods significantly.