Iterative methods for random sampling and compressed sensing recovery

In this paper, two methods are proposed which address the random sampling and compressed sensing recovery problems. The proposed random sampling recovery method is the Iterative Method with Adaptive Thresholding and Interpolation (IMATI). Simulation results indicate that the proposed method outperforms existing random sampling recovery methods such as Iterative Method with Adaptive Thresholding (IMAT). Moreover, the suggested method surpasses compressed sensing recovery methods such as Orthogonal Matching Pursuit (OMP) in terms of recovery performance. We propose a compressed sensing recovery method, named Iterative Method with Adaptive Thresholding for Compressed Sensing recovery (IMATCS). Unlike its counterpart, Iterative Hard Thresholding (IHT), the thresholding function of the proposed method is adaptive i.e. the threshold value changes with the iteration number, which enables IMATCS to reconstruct the sparse signal without having any knowledge of the sparsity number. The simulation results indicate that IMATCS outperforms IHT and OMP in both computational complexity and quality of the recovered signal.