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

arXiv: https://arxiv.org/abs/2505.08518 · HTML: https://mlsanity.com/paper/2505.08518/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 40 references that are in the map.
- First posted on arXiv 13 May 2025.

## Builds on (most cited first, 5 of 5)

- [Pattern-Coupled Sparse Bayesian Learning for Recovery of Block-Sparse Signals](https://mlsanity.com/paper/1311.2150/) (2013)
- [Iterative Bayesian Reconstruction of Non-IID Block-Sparse Signals](https://mlsanity.com/paper/1412.2316/) (2014)
- [Block Sparse Bayesian Learning: A Diversified Scheme](https://mlsanity.com/paper/2402.04646/) (2024)
- [General Total Variation Regularized Sparse Bayesian Learning for Robust Block-Sparse Signal Recovery](https://mlsanity.com/paper/2102.06845/) (2021)
- [Near/Far-Field Channel Estimation For Terahertz Systems With ELAAs: A Block-Sparse-Aware Approach](https://mlsanity.com/paper/2404.05544/) (2024)

## Abstract (arXiv)

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.