Sparsity Order Estimation for Compressed Sensing System Using Sparse Binary Sensing Matrix

Abstract

We present a composite Compressed Sensing system for the acquisition and recovery of compressible signals, where a sparse Binary Sensing Matrix aids Sparsity Order Estimation, and a Gaussian Sensing Matrix aids reconstruction. The Binary Sensing Matrix is deterministic and is adapted according to the varying nature of the sparsity order. We estimate the sparsity order by exploiting the sparse structure of the Binary Sensing Matrix and the statistics of the obtained measurements. We refine the estimates of the sparsity order using a Kalman filter with a discrete Markov model that characterizes the sparsity order variation. A Binary Sensing Matrix-Aided Orthogonal Matching Pursuit is developed for faster recovery of compressible signals. Simulation results on real-world and synthetic data demonstrate the merits of the proposed sparsity order estimation and recovery methods compared to other existing methods. Our proposed methods are practical and recover compressible signals at least 25% faster than the existing methods.

Fourier-domain image reconstruction in near-field microwave imaging using a dynamic metasurface antenna: a sparse-sampling-based approach

“…, where f N denotes the total number of frequency samples), it can be represented as a compressible signal using its sparse transform domain vector θ [26] 1 .…”

A High-Frequency Measurement Method of Downhole Vibration Signal Based on Compressed Sensing Technology and Its Application in Drilling Tool Failure Analysis

“…In the above studies, it is shown that CS technology can be used to compress the vibration data of different equipment, and can perform signal reconstruction and subsequent fault diagnosis [32][33]. The application of CS theory in vibration signal measurement has involved sparse dictionary representation of vibration signals, optimization of observation matrix, signal reconstruction, and other aspects [34][35]. However, the research on direct application to downhole vibration signal measurement is still relatively less.…”