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

TL;DR

This paper introduces SPP-SBL, a novel Bayesian learning method that adaptively captures unknown block-sparse patterns using a space power prior and an EM algorithm, improving recovery accuracy.

Contribution

It unifies existing pattern-based methods with a new variance transformation framework and proposes a space power prior to better model unknown block-sparse structures.

Findings

Successfully recovers chain-structured and multi-pattern sparse signals

Achieves significant improvements in recovery accuracy over existing methods

Effectively handles real-world multi-modal sparse signals like images and audio

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.