Coupled Quadratic Congruential Random Number Generator-Aided Measurement Matrix Construction

Compressed sensing (CS) is considered as a practical signal processing technique that can recover a sparse signal sampled by a rate much lower than the Nyquist–Shannon rate. To successfully recover that signal, CS goes through three main stages: signal representation, measurement matrix formation to signal compression, and signal reconstruction. The two conditions that need to be ensured are the sparsity of signals and the restricted isometry property of the measurement matrix. The measurement matrix plays an important role in the successful reconstruction. Indeed, the design of a good measurement matrix will improve the reconstruction rate. This article proposes a method for constructing the measurement matrix by using coupled quadratic congruential random number generator. By comparing the inequality of two quadratic congruential random number sequences, the random bit sequence +1 and −1 can be generated. The proposed method has advantages in efficient/easy hardware implementation. Then, the measurement matrix formed by this method will be proved to satisfy the CS reconstruction conditions. The simulation results also show the recovery rate of the formed measurement matrix based on the sparsity levels. At last, an implementation to a sub-Nyquist sampling scheme will be presented with the performance of reconstruction in some practical scenarios.