Analysis of the Measurement Matrices for Compressive Sensing of Signals

Compressive Sensing is a relatively new technique for acquiring signals and images. This technique is a part of sparse signal processing and it exploits sparsity of the signal in one or the other domain. The main objective of this work is to show that sparse signal can be reconstructed with a lesser number of samples than that dictated by the Nyquist criteria. This research work considers a synthetically generated time domain sparse signal, and sample it using a random measurement matrix. Then, a time domain signal, which is sparse in the frequency domain is sampled using a delta matrix. This signal is first converted to the frequency domain using DFT. It is shown in this work that the reconstruction is better when 64 samples are used as compared to when 32 samples are used in the measurements.