Randomness, Coherence and Noise Robustness in Compressive Sensing

Subject Areas : Communication

Haybert Markarian ¹ , Sedigheh Ghofrani ²

1 - Department of Electrical Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran.
2 - Department of Electrical Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran.

Received: 2019-12-22 Accepted : 2020-02-08 Published : 2020-03-01

Keywords: coherence, Compressive sensing (CS), Noiselets, randomness, Noise Robust,

Abstract :

The theory of compressive sensing (CS) in contrast with well-known Nyquist sampling theorem was proposed. Sensing matrix and sparse matrix have key roles in perfect signal reconstruction by using either greedy algorithms like orthogonal matching pursuit (OMP) or -norm based methods. In this paper, different pairs as sensing and sparse matrices are evaluated in terms of randomness and coherence. Noiselet as a complex measurement matrix has low coherence with Haar wavelet, and so the recovered images by OMP in comparison with other measurement-sparse matrices are appropriate. But, because of complexity, it cannot be used for big size images. However, the pair structured random sensing matrix with values 0, 1 and Fourier sparse matrix which got the second rank in terms of coherence, approved to be a noise robust pair and showed a great potential to be used in CS.