提出新方法SPP-SBL，高效恢复未知结构的块稀疏信号
SPP-SBL: Space-Power Prior Sparse Bayesian Learning for Block Sparse Recovery
- 基于无向图建模空间耦合，自适应捕捉块稀疏信号结构
- 通过高阶方程求根与EM算法结合，解决参数估计难题
- 在图像、音频等真实信号上表现优异，适合结构化信号重建场景
未知结构模式下块稀疏信号的恢复仍是结构化稀疏信号重构中的基本挑战。本文提出一种方差变换框架，统一现有基于模式的块稀疏贝叶斯学习方法，并引入基于无向图模型的空间幂先验，以自适应捕获块稀疏信号的未知结构。通过将EM算法与高阶方程求根相结合，提出新型结构化稀疏贝叶斯学习方法SPP-SBL，有效解决了基于模式方法中空间耦合参数估计这一开放问题。进一步证明，学习空间耦合参数的相对值是捕捉未知块稀疏结构、提升恢复精度的关键。实验验证了SPP-SBL可成功恢复多种复杂结构稀疏信号（如链式结构、多模式稀疏信号）及真实世界多模态结构稀疏信号（图像、音频），在多个指标上显著优于现有方法。
原文摘要 · Abstract (English)
The recovery of block-sparse signals with unknown structural patterns remains a fundamental challenge in structured sparse signal reconstruction. By proposing a variance transformation framework, this paper unifies existing pattern-based block sparse Bayesian learning methods, and introduces a novel space power prior based on undirected graph models to adaptively capture the unknown patterns of block-sparse signals. By combining the EM algorithm with high-order equation root-solving, we develop a new structured sparse Bayesian learning method, SPP-SBL, which effectively addresses the open problem of space coupling parameter estimation in pattern-based methods. We further demonstrate that learning the relative values of space coupling parameters is key to capturing unknown block-sparse patterns and improving recovery accuracy. Experiments validate that SPP-SBL successfully recovers various challenging structured sparse signals (e.g., chain-structured signals and multi-pattern sparse signals) and real-world multi-modal structured sparse signals (images, audio), showing significant advantages in recovery accuracy across multiple metrics.
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