A Novel Measurement Matrix Based on Regression Model for Block Compressed Sensing

This paper proposes a novel generator of the measurement matrix for block compressed sensing (BCS), which is resulted by the regression model between the coordinates of pixels and their gray level. Our algorithm has three main advantages: (1) Speedy. the computation of our algorithm is the same as yielding a random Gaussian measurement matrix, which is often used in BCS. (2) High rate of accuracy. Our measurement matrix has more mathematical meaning, because it is resulted from the regression between the coordinates of pixels and their gray level. (3) Good compliance. Replacing immediately the random Gaussian measurement matrix by the proposed measurement matrix can significantly improve the performance of existing frameworks like smooth projected Landweber (SPL). Simulation results show that our measurement matrix can improve average 2-3 dB PSNR in BCS-SPL framework, in which random Gaussian matrix is often used as measurement matrix.