Structural optimization of measurement matrix in image reconstruction based on compressed sensing

Abstract

In image reconstruction based on the compressed sensing (CS), linear measurement on the image is required, and the original signal is not only sampled and compressed by the measurement, but also the signal dimension is greatly reduced. Then the original signal is reconstructed from the measured value by the reconstruction algorithm, so the structure of the measurement matrix not only affects the results of the measurement, but also directly relates to the reconstruction quality of the image. This paper redesign measurement matrix based on two valued random measurement matrix and construct a very sparse diagonal block measurement matrix. New measurement matrix greatly improves the non-correlation of measurement matrix and reduces the condition number of sensing matrix, which makes the sensing matrix better satisfy the RIP Condition (the Restricted Isometry Property) and is more conducive to signal reconstruction. The new measurement matrix is not only easy to implement on the hardware and application in engineering conveniently and directly, but also can improve the speed and accuracy of image reconstruction. Simulation results show that, when the sampling rate is from 0.1 to 0.5, peak signal to noise ratio (PSNR) of the reconstructed image is increased from 1 to 4dB.