二维谐波恢复问题的贝叶斯新方法
A Novel Bayesian Approach for the Two-Dimensional Harmonic Retrieval Problem
摘要：
稀疏信号恢复算法（如稀疏贝叶斯学习）工作良好，但在处理高维参数字典时，复杂度会迅速增长。在这项工作中，我们提出了一种新的贝叶斯策略来解决二维谐波恢复问题，通过重塑和重新参数化的标准数据模型。这个新的模型允许我们引入一个块稀疏结构的方式，使一个自然配对的参数在两个维度。数值模拟表明，推理算法（H-MSBL）不受源可识别性问题，并能够估计谐波分量在具有挑战性的情况下，同时保持低的计算复杂度。
英文摘要：
Sparse signal recovery algorithms like sparse Bayesian learning work well but the complexity quickly grows when tackling higher dimensional parametric dictionaries. In this work we propose a novel Bayesian strategy to address the two dimensional harmonic retrieval problem, through remodeling and reparameterization of the standard data model. This new model allows us to introduce a block sparsity structure in a manner that enables a natural pairing of the parameters in the two dimensions. The numerical simulations demonstrate that the inference algorithm developed (H-MSBL) does not suffer from source identifiability issues and is capable of estimating the harmonic components in challenging scenarios, while maintaining a low computational complexity.
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