# A Unitary Transform Based Generalized Approximate Message Passing

arXiv: https://arxiv.org/abs/2210.08861 · HTML: https://mlsanity.com/paper/2210.08861/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 25 references that are in the map.
- First posted on arXiv 17 Oct 2022.

## Builds on (most cited first, 3 of 3)

- [A GAMP Based Low Complexity Sparse Bayesian Learning Algorithm](https://mlsanity.com/paper/1703.03044/) (2017)
- [Unitary Approximate Message Passing for Sparse Bayesian Learning](https://mlsanity.com/paper/2101.09954/) (2021)
- [A comment on the "A unified Bayesian inference framework for generalized linear models"](https://mlsanity.com/paper/1904.04485/) (2019)

## Built on by (most cited first, 1 of 1)

- [QCM-SGM+: Improved Quantized Compressed Sensing With Score-Based Generative Models](https://mlsanity.com/paper/2302.00919/) (2023)

## Abstract (arXiv)

We consider the problem of recovering an unknown signal mathbf x∈ mathbb Rn from general nonlinear measurements obtained through a generalized linear model (GLM), i.e., mathbf y= fleft(mathbf Amathbf x+mathbf wright), where f(·) is a componentwise nonlinear function. Based on the unitary transform approximate message passing (UAMP) and expectation propagation, a unitary transform based generalized approximate message passing (GUAMP) algorithm is proposed for general measurement matrices bfA, in particular highly correlated matrices. Experimental results on quantized compressed sensing demonstrate that the proposed GUAMP significantly outperforms state-of-the-art GAMP and GVAMP under correlated matrices bfA.