Hybrid wavelet measurement matrices for improving compressive imaging

Compressive sensing principle claims that a compressible signal can be recovered from a small number of random linear measurements. However, the design of efficient measurement basis in compressive imaging remains as a challenging problem. In this paper, a new set of hybrid wavelet measurement matrices is proposed to improve the quality of the compressive imaging, increase the compression ratio and reduce the processing time. The performance of these hybrid wavelet matrices for image modeling and reconstruction is evaluated and compared with other traditional measurement matrices such as the random measurement matrices, Walsh and DCT matrices. The compressive imaging approach chosen in this study is the block compressive sensing with smoothed projected Landweber reconstruction technique. The simulation results indicate that the imaging performance of the proposed hybrid wavelet measurement matrices is approximately 2-3 dB better than that obtained using Gaussian matrix especially at higher compression ratios.