The construction of measurement matrices based on block weighing matrix in compressed sensing

• A structured measurement matrix for practice compressed sensing is proposed.
• The measurement matrix is mainly based on block weighing matrix.
• The measurement matrix has high sparsity and block circulant structure.
• The performance of the measurement matrix is proved to be near optimal.
• Chaos-based permutation operator is introduced for hardware implementation.

In this paper, we propose a new structured measurement matrix for practical compressed sensing based on block weighing matrix, called partial Random Block Weighing Matrix (pRBWM). The proposed pRBWM is universal with a variety of sparse signals and provides high reconstruction performance simultaneously. In addition, with the sparse and circulant block structure, these new measurement matrices feature low-memory requirement and low computational complexity in reconstruction. Moreover, it can be more easily implemented in hardware thanks to its sample elements and the application of Chaos-based permutation operator in construction of pRBWM. Simulation results demonstrate that the proposed pRBWM performs comparably to, or even better than completely random matrices and many other structured matrices. And the proposed pRBWM forms a high balance between reconstruction performance,storage and computational complexity and hardware implementation.