Maximum Likelihood Estimation of Time-Varying Sparsity Level for Dynamic Sparse Signals

In the field of Compressed Sensing, estimation of sparsity level is very essential as the sparsity level determines the minimum number of (i) measurements to be obtained of a sparse signal during acquisition and (ii) iterations to be performed for many of the greedy techniques for the perfect recovery of the sparse signal from the obtained measurements. In this paper, we propose a Maximum Likelihood (ML) estimator to estimate the instantaneous sparsity level during acquisition and an ML sequence (MLS) estimator of sparsity levels during recovery. As the sparsity level varies in time due to the continuous birth of newer supporting components and death of existing supporting components, this paper models the sparsity level variation as a stochastic birth-death process. The real-world applications of the proposed estimators are presented on the compression of aircraft vibration signals and the estimation of wireless channels. The simulation results on real-world and model-generated data demonstrate the performance merits of the proposed estimators compared to other existing methods.