# Interleaved Block-Sparse Transform

arXiv: https://arxiv.org/abs/2407.13255 · HTML: https://mlsanity.com/paper/2407.13255/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jul 2024.

## Built on by (most cited first, 2 of 2)

- [Random Multiplexing](https://mlsanity.com/paper/2512.24087/) (2025)
- [Diffusion-OAMP for Joint Image Compression and Wireless Transmission](https://mlsanity.com/paper/2604.27952/) (2026)

## Abstract (arXiv)

Low-complexity Bayes-optimal memory approximate message passing (MAMP) is an efficient signal estimation algorithm in compressed sensing and multicarrier modulation. However, achieving replica Bayes optimality with MAMP necessitates a large-scale right-unitarily invariant transformation, which is prohibitive in practical systems due to its high computational complexity and hardware costs. To solve this difficulty, this letter proposes a low-complexity interleaved block-sparse (IBS) transform, which consists of interleaved multiple low-dimensional transform matrices, aimed at reducing the hardware implementation scale while mitigating performance loss. Furthermore, an IBS cross-domain memory approximate message passing (IBS-CD-MAMP) estimator is developed, comprising a memory linear estimator in the IBS transform domain and a non-linear estimator in the source domain. Numerical results show that the IBS-CD-MAMP offers a reduced implementation scale and lower complexity with excellent performance in IBS-based compressed sensing and interleave frequency division multiplexing systems.