SPP-SBL: Space-Power Prior Sparse Bayesian Learning for Block Sparse Recovery

• URL: http://arxiv.org/abs/2505.08518v1
• Date: Tue, 13 May 2025 12:49:25 GMT
• Title: SPP-SBL: Space-Power Prior Sparse Bayesian Learning for Block Sparse Recovery
• Authors: Yanhao Zhang, Zhihan Zhu, Yong Xia,
• Abstract summary: This paper introduces a novel space power prior based on undirected graph models to adaptively capture the unknown patterns of block-sparse signals.<n>We develop a new structured sparse Bayesian learning method, which effectively addresses the open problem of space coupling parameter estimation.
• Score: 16.61484758008309
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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