利用组稀疏性的结构化线谱变分推断
Variational Inference of Structured Line Spectra Exploiting Group-Sparsity
AI总结：
提出一种变分推断算法，利用组稀疏性分层先验模型将信号分解为多组相关谱线，联合估计组参数及数量，在多基频估计等三个推断问题上优于现有算法。
摘要：
在本文中，我们提出了一种变分推断算法，该算法将信号分解为多组相关的谱线。每组中的谱线与该组内所有谱线共有的一个组参数相关联。所提出的算法利用促进稀疏解的 Bernoulli-Gamma-Gaussian 分层先验模型，联合估计组参数、组内谱线数量以及组的数量。旨在最大化证据下界（ELBO），变分推断提供了后验概率密度函数（PDFs）的解析近似，并给出了额外模型参数（如测量噪声方差）的估计。虽然组的激活变量和相关联的组参数（如基频及相应的更高阶谐波）被估计为点估计，但其余参数（如谱线的复振幅及其精度参数）则被估计为近似后验 PDFs。我们在三个不同的推断问题上展示了所提出算法的通用性和性能。具体而言，使用合成测量将所提出的算法应用于多基频估计问题、基于雷达信号的扩展目标估计问题以及变分模态分解（VMD），并使用 Bach-10 数据集应用于真实的多基频估计问题。结果表明，所提出的算法在所有三个推断问题上均优于最先进的基于模型和预训练的算法。
英文摘要：
In this paper, we present a variational inference algorithm that decomposes a signal into multiple groups of related spectral lines. The spectral lines in each group are associated with a group parameter common to all spectral lines within the group. The proposed algorithm jointly estimates the group parameters, the number of spetral lines within a group, and the number of groups exploiting a Bernoulli-Gamma-Gaussian hierarchical prior model which promotes sparse solutions. Aiming to maximize the evidence lower bound (ELBO), variational inference provides analytic approximations of the posterior probability density functions (PDFs) and also gives estimates of the additional model parameters such as the measurement noise variance. While the activation variables of the groups and the associated group parameters (such as fundamental frequencies and the corresponding higher order harmonics) are estimated as point estimates, the remaining parameters such as the complex amplitudes of the spectral lines and their precision parameters are estimated as approximate posterior PDFs. We demonstrate the versatility and performance of the proposed algorithm on three different inference problems. In particular, the proposed algorithm is applied to the multi-pitch estimation problem, the radar signal-based extended object estimation problem, and variational mode decomposition (VMD) using synthetic measurements and to real multi-pitch estimation problem using the Bach-10 dataset. The results show that the proposed algorithm outperforms state-of-the-art model-based and pre-trained algorithms on all three inference problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
