Compressed Sensing: A Simple Deterministic Measurement Matrix and a Fast Recovery Algorithm

Compressed sensing (CS) is a technique that is suitable for compressing and recovering signals having sparse representations in certain bases. CS has been widely used to optimize the measurement process of bandwidth and power constrained systems like wireless body sensor network. The central issues with CS are the construction of measurement matrix and the development of recovery algorithm. In this paper, we propose a simple deterministic measurement matrix that facilitates the hardware implementation. To control the sparsity level of the signals, we apply a thresholding approach in the discrete cosine transform domain. We propose a fast and simple recovery algorithm that performs the proposed thresholding approach. We validate the proposed method by compressing and recovering electrocardiogram and electromyogram signals. We implement the proposed measurement matrix in a MSP-EXP430G2 LaunchPad development board. The simulation and experimental results show that the proposed measurement matrix has a better performance in terms of reconstruction quality compared with random matrices. Depending on the compression ratio, it improves the signal-to-noise ratio of the reconstructed signals from 6 to 20 dB. The obtained results also confirm that the proposed recovery algorithm is, respectively, 23 and 12 times faster than the orthogonal matching pursuit (OMP) and stagewise OMP algorithms.