Compressed Sensing Natural Imaging via Hadamard-Diagonal Matrix

The measurement matrix is one of the keys of the compressed sensing. However, the existing measurement matrices face the two main problems of the difficult hardware implementation and the low sensing efficiency. In fact, those matrices always ignore the energy concentration characteristic of the natural images in the sparse domain, which greatly limits the sensing efficiency of the measurement matrices and thus the construction efficiency. In this paper, we propose a simple but efficient measurement matrix based on the Hadamard matrix with the consideration of maximizing the energy conservation in the sparse domain, named Hadamard-Diagonal Matrix (HDM). We keep the main sensing rows and columns in the Hadamard matrix with '1' and the others with '0' to keep more energy after the sampling of the natural images in the sparse domain, which increases the sensing efficiency. Meanwhile, the HDM is a binary and sparse matrix which benefits the hardware implementation. The experimental results show that the HDM performs better than some popular existing measurement matrices and is incoherent with different sparse basis.