  Gaussian random matrix (GRM) has been widely used to generate linear
measurements in compressed sensing (CS) of natural images. However, there
actually exist two disadvantages with GRM in practice. One is that GRM has
large memory requirement and high computational complexity, which restrict the
applications of CS. Another is that the CS measurements randomly obtained by
GRM cannot provide sufficient reconstruction performances. In this paper, a
Deep neural network based Sparse Measurement Matrix (DSMM) is learned by the
proposed convolutional network to reduce the sampling computational complexity
and improve the CS reconstruction performance. Two sub networks are included in
the proposed network, which are the sampling sub-network and the reconstruction
sub-network. In the sampling sub-network, the sparsity and the normalization
are both considered by the limitation of the storage and the computational
complexity. In order to improve the CS reconstruction performance, a
reconstruction sub-network are introduced to help enhance the sampling
sub-network. So by the offline iterative training of the proposed end-to-end
network, the DSMM is generated for accurate measurement and excellent
reconstruction. Experimental results demonstrate that the proposed DSMM
outperforms GRM greatly on representative CS reconstruction methods
