The reconstruction of sparse signal is an active area of research. Different from a typical i.i.d. assumption, this paper considers a non-independent prior of group structure. For this more practical setup, we propose EM-aided HyGEC, a new algorithm to address the stability issue and the hyper-parameter issue facing the other algorithms. The instability problem results from the ill condition of the transform matrix, while the unavailability of the hyper-parameters is a ground truth that their values are not known beforehand. The proposed algorithm is built on the paradigm of HyGAMP (proposed by Rangan et al .) but we replace its inner engine, the GAMP, by a matrix-insensitive alternative, the GEC, so that the first issue is solved. For the second issue, we take expectation-maximization as an outer loop, and together with the inner engine HyGEC, we learn the value of the hyper-parameters. Effectiveness of the proposed algorithm is also verified by means of numerical simulations.

中文翻译：

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期望最大化辅助的混合广义期望在稀疏信号重构中的一致性

稀疏信号的重建是研究的活跃领域。与典型的iid假设不同，本文考虑了群体结构的非独立先验。对于这种更实际的设置，我们提出了EM辅助的HyGEC，这是一种解决其他算法所面临的稳定性问题和超参数问题的新算法。不稳定性问题是由变换矩阵的不良条件引起的，而超参数的不可用性是一个事实，即它们的值事先未知。提出的算法建立在HyGAMP范式的基础上（由Rangan提出）。等 。），但我们用对矩阵不敏感的替代方案GEC替换了其内部引擎GAMP，从而解决了第一个问题。对于第二个问题，我们将期望最大化作为一个外部循环，并与内部引擎HyGEC一起学习超参数的值。数值仿真也验证了所提算法的有效性。