Performance Improvement of Orthogonal Matching Pursuit Based on Wilkinson Matrix for Block Compressive Sensing

Compressed sensing is a new paradigm to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper, a new structured Wilkinson matrix is proposed as a measurement matrix to improve the performance of the block compressive sensing technique which is based on the orthogonal matching pursuit (OMP) algorithm. OMP is simpler to implement and potentially faster than linear programming algorithms but it suffers from two problems: the lack of reconstruction quality, and the need for a large number of measurements. The use of the new structured Wilkinson matrix has improved the OMP reconstruction quality, increased the compression ratio and reduced the computational time. In our experiments, the proposed method was applied to three different test images: Lenna, Barbara and heart MRI. Compared to conventional CS algorithms, the proposed method improves the reconstruction quality by approximately 10 dB with less computational time.