Compressive sampling and reconstruction in shift-invariant spaces associated with the fractional Gabor transform

Abstract

In this paper, we propose a compressive sampling and reconstruction system based on the shift-invariant space associated with the fractional Gabor transform. With this system, we aim to achieve the sub-Nyquist sampling and accurate reconstruction for chirp-like signals containing time-varying characteristics. Under the proposed scheme, we introduce the fractional Gabor transform to make a stable expansion for signals in the joint time-fractional-frequency domain. Then the compressive sampling and reconstruction system is constructed under the compressive sensing and shift-invariant space theory. We establish the reconstruction model and propose a block multiple response extension of sparse Bayesian learning algorithm to improve the reconstruction effect. The reconstruction error for the proposed system is analyzed. We show that, with considerations of noises and mismatches, the total error is bounded. The effectiveness of the proposed system is verified by numerical experiments. It is shown that our proposed system outperforms the other systems state-of-the-art.

Keywords

• Compressive sampling
• Reconstruction
• Shift-invariant space
• Fractional gabor transform
• Chirp-like signals