Compressive sensing matrix designed by tent map, for secure data transmission

Abstract

The approach between compressive sensing and chaotic behaviour is a new technique in order to capture signals at sub-Nyquist rate. For recovering the original signal from the sampled one it is necessary to use the computing power because a specific matrix is needed to implement the sensing procedure. This matrix has to respect the Restricted Isometry Property (RIP). In this paper a way to generate this matrix is presented by using the tent map. The aim is to show that for any initial condition or parameter the performances, in order to generate a sensing matrix, are similar. In a secure data transmission, these two values will be known only by the emitter and receiver. At each new sent signal the initial condition and the parameter will be changed.