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

Abstract

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.Index Terms-Compressed sensing (CS), deterministic measurement matrix, electrocardiogram (ECG), electromyogram (EMG), recovery algorithm.

Comparison of Compression Solutions for Impedance and Field Potential Signals of Cardiomyocytes

“…The more incoherent the sensing matrix is with the dictionary, the greater the reconstruction of the signal will be. The deterministic Binary Block Diagonal matrix [6] presents the best incoherence.…”

“…We selected the cosinus basis and tested different sensing matrix such as Gaussian, Binary and Binary Block Diagonal matrices [6]. Then, we selected Basis Pursuit (BP) for the reconstruction algorithm.…”

Semitensor Product Compressive Sensing for Big Data Transmission in Wireless Sensor Networks

“…From (5), the dimension of is / , so the compression ratio is = ( / )/ = / , where and are the row number and column number of the STP-CS measurement matrix, respectively. From (12), the range of compression ratio of STP-CS is log( / )/ ⩽ / < 1. And the compression ratio of the traditional CS is = / , where is the row number of the traditional CS measurement matrix, and is the dimension of the signal.…”

“…Another kind of CS encryption can save storage space by storing matrix generation parameters as the secret key rather than the whole matrix [11,12]. This kind of CS encryption generates matrices by deterministic methods such as algebraic curves [13], coding (LDPC, BCH) [14], and chaotic systems (Chebyshev, Logistic, and Tent) [15,16]; it can save huge storage space compared with keeping the whole matrix.…”

Investigation of Kronecker-based Recovery in Compressive Sensing

“…Moreover, the number of multiplications needed to be performed is 0. In comparison, generation of most of the random matrices require M × N multiplications [35].…”