Simultaneous Bayesian Sparse Approximation With Structured Sparse Models
Simultaneous Bayesian Sparse Approximation With Structured Sparse Models
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DOI：
10.1109/tsp.2016.2605067
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发表时间：
2016-12
影响因子：
5.4
通讯作者：
Wei Chen;D. Wipf;Yu Wang;Yang Liu;I. Wassell
中科院分区：
文献类型：
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作者：
Wei Chen;D. Wipf;Yu Wang;Yang Liu;I. Wassell
稀疏近似是许多信号处理、图像处理和机器学习应用的关键。如果多个信号保持某种程度的依赖性，例如，支持集在统计上相关，则与单独求解每个信号相反，从测量向量联合估计稀疏表示向量通常将是有利的。在本文中，我们提出了同时稀疏贝叶斯学习（SBL）的联合稀疏近似与两个结构化稀疏模型（SSM），其中一个是行稀疏嵌入元素稀疏，另一个是行稀疏加元素稀疏。虽然SBL作为处理单个稀疏逼近问题的一种手段引起了人们的广泛关注，但如何将SBL扩展到SSM并不明显。通过利用SM的现有凸方法的双空间视图，我们展示了SSM的精度分量模型和协方差分量模型，其中两个模型都涉及一个共同的超参数和一个创新超参数，它们共同控制每个系数的先验方差。精度分量与协方差分量模型的统计视角揭示了SSM的内在机制，也导致了我们对SSM的SBL启发成本函数的发展。集中式算法，包括11和12重加权算法和基于共识的分散式算法开发的同时稀疏逼近与SSM。此外，理论分析提供了宝贵的见解，提出的方法，其中包括全局极小值分析的SBL启发的非凸成本函数和收敛性分析的建议11重加权算法的SSM。数值实验证明了所提算法的上级性能。
Sparse approximation is key to many signal processing, image processing, and machine learning applications. If multiple signals maintain some degree of dependency, for example, the support sets are statistically related, then it will generally be advantageous to jointly estimate the sparse representation vectors from the measurement vectors as opposed to solving for each signal individually. In this paper, we propose simultaneous sparse Bayesian learning (SBL) for joint sparse approximation with two structured sparse models (SSMs), where one is row-sparse with embedded element-sparse and the other one is row-sparse plus element-sparse. While SBL has attracted much attention as a means to deal with a single sparse approximation problem, it is not obvious how to extend SBL to SSMs. By capitalizing on a dual-space view of existing convex methods for SMs, we showcase the precision component model and covariance component model for SSMs, where both models involve a common hyperparameter and an innovation hyperparameter that together control the prior variance for each coefficient. The statistical perspective of precision component versus covariance component models unfolds the intrinsic mechanism in SSMs, and also leads to our development of SBL-inspired cost functions for SSMs. Centralized algorithms that include 11 and 12 reweighting algorithms and consensus-based decentralized algorithms are developed for simultaneous sparse approximation with SSMs. In addition, theoretical analysis is conducted to provide valuable insights into the proposed approach, which includes global minima analysis of the SBL-inspired nonconvex cost functions and convergence analysis of the proposed 11 reweighting algorithms for SSMs. Superior performance of the proposed algorithms is demonstrated by numerical experiments.