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

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.