Low storage space for compressive sensing: semi-tensor product approach

Random measurement matrices play a critical role in successful recovery with the compressive sensing (CS) framework. However, due to its randomly generated elements, these matrices require massive amounts of storage space to implement a random matrix in CS applications. To effectively reduce the storage space of the random measurement matrix for CS, we propose a random sampling approach for the CS framework based on the semi-tensor product (STP). The proposed approach generates a random measurement matrix, where the dimensions of the random measurement matrix are reduced to a quarter (or 1/16, 1/64, and even 1/256) of the number of dimensions, which are used for conventional CS. We then estimate the values of the sparse vector with a modified iteratively re-weighted least-squares (IRLS) algorithm. The results of numerical simulations showed that the proposed approach can reduce the storage space of a random matrix to at least a quarter while maintaining quality of reconstruction. All results confirmed that the proposed approach significantly influences the physical implementation of the CS in images, especially on embedded system and field programmable gate array (FPGA), where storage is limited.