A new method of sensing matrix optimization for compressive sensing

Abstract

Compressive sensing (CS) as a new signal acquisition protocol has been applied widely in numerous application areas such as medical imaging, cryptography, biometrics, communications, wireless sensor networks and internet of things. One problem of CS systems is how to design a suitable sensing matrix to improve the signal reconstruction accuracy with the same number of measurements. The recent method to optimize the sensing matrix is by minimizing the mutual coherence of the equivalent dictionary and the amplified sparse representation error (SRE). This paper proposes a new method of sensing matrix optimization by introducing the relative amplified SRE parameter and incorporate it into the optimization problem. The experimental results with test patches and natural images show that the CS system by using the proposed optimized sensing matrix can decrease the mutual coherence and the amplified SRE. The PSNR of reconstructed test patches and natural images for 25% compression ratio are 27.06 dB and 28.32 dB respectively. The results also demonstrate that the proposed method outperforms the previous ones in terms of image reconstruction accuracy.