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.

在本文中，我们提出了一种基于与分数 Gabor 变换相关的移位不变空间的压缩采样和重建系统。通过该系统，我们的目标是实现对包含时变特征的类啁啾信号的亚奈奎斯特采样和精确重建。在所提出的方案下，我们引入了分数 Gabor 变换，以对联合时-分数-频域中的信号进行稳定扩展。然后在压缩感知和位移不变空间理论下构建压缩采样和重建系统。我们建立了重建模型，并提出了稀疏贝叶斯学习算法的块多响应扩展，以提高重建效果。分析了所提出系统的重构误差。我们表明，考虑到噪声和失配，总误差是有界的。通过数值实验验证了所提出系统的有效性。结果表明，我们提出的系统优于其他最先进的系统。