  The compressed sensing (CS) theory has been successfully applied to image
compression in the past few years as most image signals are sparse in a certain
domain. Several CS reconstruction models have been recently proposed and
obtained superior performance. However, there still exist two important
challenges within the CS theory. The first one is how to design a sampling
mechanism to achieve an optimal sampling efficiency, and the second one is how
to perform the reconstruction to get the highest quality to achieve an optimal
signal recovery. In this paper, we try to deal with these two problems with a
deep network. First of all, we train a sampling matrix via the network training
instead of using a traditional manually designed one, which is much appropriate
for our deep network based reconstruct process. Then, we propose a deep network
to recover the image, which imitates traditional compressed sensing
reconstruction processes. Experimental results demonstrate that our deep
networks based CS reconstruction method offers a very significant quality
improvement compared against state of the art ones.
