Abstract In this paper, a Bayesian model is adopted for sparse signal recovery where sparsity is enforced on the reconstructed coefficients via probabilistic priors. In particular, we focus on a group spike-and-slab prior and a kernel matrix which capture both the underlying group structure and the element correlation within groups. A novel greedy based group adaptive matching pursuit (GAMP) algorithm is introduced, which integrates both prior parameter learning and intra-group correlation parameter learning into one single problem. The proposed approach improves the reconstruction accuracy and offers strong robustness to signal-to-noise ratio. We consider a fast implementation method of GAMP which applies the preconditioned conjugate gradient method. Simulations, MNIST dataset based experiments and multi-static radar imaging application are used to verify the superior performance of the proposed method over existing techniques.

中文翻译：

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用于稀疏信号恢复的组内相关学习的组自适应匹配追踪

摘要 在本文中，采用贝叶斯模型进行稀疏信号恢复，其中通过概率先验对重构系数进行稀疏化。特别是，我们专注于组尖峰和板坯先验和内核矩阵，它们捕获了底层的组结构和组内的元素相关性。介绍了一种新的基于贪婪的群自适应匹配追踪（GAMP）算法，它将先验参数学习和组内相关参数学习集成到一个问题中。所提出的方法提高了重建精度，并对信噪比提供了很强的鲁棒性。我们考虑应用预处理共轭梯度法的 GAMP 的快速实现方法。模拟，