Abstract Conventional Bayesian compressive sensing (CS) is considered for signals that are sparse in some domains, and only sparse prior is adopted to guarantee the exact inverse recovery. However, many additional statistical structures of the signals are naturally available, such as the group structure and the tree structure. In this paper, a novel multi-task structured Bayesian compressive sensing (MTSBCS) algorithm based on a hierarchical Bayesian model is proposed to recover sparse signal, with the exploitation of both intra-group correlation and underlying continuous structure. In this model, two Toeplitz matrix are used to model such intra-group correlation and underlying continuous structure, respectively. According to the proposed generative model, a greedy-based adaptive matching pursuit technique is then introduced to perform the inference for this non-convex optimization problem. Simulations and experimental results show the superiorities of the proposed MTSBCS over several state-of-the-art algorithms.

中文翻译：

---

利用信号结构的多任务贝叶斯压缩感知

摘要 传统的贝叶斯压缩感知（CS）被考虑用于某些域稀疏的信号，仅采用稀疏先验来保证精确的逆恢复。然而，信号的许多附加统计结构自然是可用的，例如组结构和树结构。在本文中，提出了一种基于分层贝叶斯模型的新型多任务结构化贝叶斯压缩感知 (MTSBCS) 算法来恢复稀疏信号，同时利用组内相关性和底层连续结构。在这个模型中，两个 Toeplitz 矩阵分别用于对这种组内相关性和底层连续结构进行建模。根据提出的生成模型，然后引入了一种基于贪婪的自适应匹配追踪技术来对这个非凸优化问题进行推理。模拟和实验结果表明，所提出的 MTSBCS 优于几种最先进的算法。