Adaptive Cluster Structured Sparse Bayesian Learning with Application to Compressive Reconstruction for Chirp Signals

Abstract

Compressive sensing (CS) is a promising framework to achieve efficient sampling for wide-band chirp signals due to its significance in reducing the sampling rate and power consumption. Under the CS theory, this paper studies the compressive reconstruction problem for chirp signals whose sparse matrix shows unknown cluster structures. To investigate the structure information to improve the reconstruction performance, existing methods require the prior knowledge on the cluster structure and suffer from the model mismatch problem. In this paper, an adaptive cluster structured sparse Bayesian learning algorithm is proposed to alleviate the requirements on the prior knowledge by exploiting and incorporating the local structure of the sparse matrix into the reconstruction model. To avoid the model mismatch problem, we apply an adaptive mechanism in variable estimation so that the reconstruction for one coefficient can selectively use the statistical information of its neighbors. The proposed algorithm is verified on both the simulated and the real chirp datasets. Numerical experimental results show that the proposed algorithm outperforms other state-of-art reconstruction algorithms in both noiseless and noisy environments. The proposed method is also found to further reduce the total sampling rate of the compressive sampling system.