Adaptive sparsity-aware parameter vector reconstruction with application to compressed sensing

Compressive Sensing is the idea of sampling a compressible signal below the Nyquist rate while still allowing the exact or near exact reconstruction of the original signal. The challenge is how the original signal could be recovered from a few linear observations. Recently, many reconstruction algorithms have been proposed which mostly rely on computationally costly batch-based estimation which lacks the ability of estimating changes in the signal to be reconstructed. In this paper, a recursive reconstruction algorithm is proposed which has the ability of sequentially utilizing the received observations and so capable of tracking the time varying underlying sparse or compressible signals, while, Due to the adaptive structure, the computational cost is spread out in time iterations. Simulation tests compare the performance of the proposed and state of the art algorithms.