# Iterative Bayesian Reconstruction of Non-IID Block-Sparse Signals

arXiv: https://arxiv.org/abs/1412.2316 · HTML: https://mlsanity.com/paper/1412.2316/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2014.

## Built on by (most cited first, 3 of 3)

- [Multi-bit Distributed Detection of Sparse Stochastic Signals over Error-Prone Reporting Channels](https://mlsanity.com/paper/2411.03612/) (2024)
- [Spectral Unmixing of Hyperspectral Images Based on Block Sparse Structure](https://mlsanity.com/paper/2204.04638/) (2022)
- [SPP-SBL: Space-Power Prior Sparse Bayesian Learning for Block Sparse Recovery](https://mlsanity.com/paper/2505.08518/) (2025)

## Abstract (arXiv)

This paper presents a novel Block Iterative Bayesian Algorithm (Block-IBA) for reconstructing block-sparse signals with unknown block structures. Unlike the existing algorithms for block sparse signal recovery which assume the cluster structure of the nonzero elements of the unknown signal to be independent and identically distributed (i.i.d.), we use a more realistic Bernoulli-Gaussian hidden Markov model (BGHMM) to characterize the non-i.i.d. block-sparse signals commonly encountered in practice. The Block-IBA iteratively estimates the amplitudes and positions of the block-sparse signal using the steepest-ascent based Expectation-Maximization (EM), and optimally selects the nonzero elements of the block-sparse signal by adaptive thresholding. The global convergence of Block-IBA is analyzed and proved, and the effectiveness of Block-IBA is demonstrated by numerical experiments and simulations on synthetic and real-life data.