A block-wise random sampling approach: Compressed sensing problem

The focus of this paper is to consider the compressed sensing problem. It is stated that the compressed sensing theory, under certain conditions, helps relax the Nyquist sampling theory and takes smaller samples. One of the important tasks in this theory is to carefully design measurement matrix (sampling operator). Most existing methods in the literature attempt to optimize a randomly initialized matrix with the aim of decreasing the amount of required measurements. However, these approaches mainly lead to sophisticated structure of measurement matrix which makes it very difficult to implement. In this paper we propose an intermediate structure for the measurement matrix based on random sampling. The main advantage of block-based proposed technique is simplicity and yet achieving acceptable performance obtained through using conventional techniques. The experimental results clearly confirm that in spite of simplicity of the proposed approach it can be competitive to the existing methods in terms of reconstruction quality. It also outperforms existing methods in terms of computation time.