Construction of compressive measurement matrix based on sinusoidal function called Sinusoidal Sensing Matrix (SSM)

Abstract

Compression sensing theory enables a safe reconstruction of signals under certain conditions. Random measurement (sensing) matrix Φ is one of the necessary conditions which give a strong impact on the behavior of the method used to reconstruct the signal. A deterministic method is therefore proposed to construct a new matrix called Sinusoidal Sensing Matrix (SSM) for compressing sensing theorem. The SSM matrix depends on its built upon generating equation used both Sin and Cos function depend upon the number of compressed samples. This new matrix is very simple and easy to create but very effective and can be generated in transmission and distention end without a need to send it, only need in Rx side knowledge of signal length. The new matrix interval meets the Restricted Isometry Property (RIP) characteristic with high probability.The simulation experiments of one- and two- dimensional signals, using a new matrix show a superior in evaluating recovered signals with parameters and the visual effect of the restored images.