# D-VDAMP: Denoising-based Approximate Message Passing for Compressive MRI

arXiv: https://arxiv.org/abs/2010.13211 · HTML: https://mlsanity.com/paper/2010.13211/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Oct 2020.

## Built on by (most cited first, 5 of 5)

- [Denoising Generalized Expectation-Consistent Approximation for MR Image Recovery](https://mlsanity.com/paper/2206.05049/) (2022)
- [Fast and Robust Phase Retrieval via Deep Expectation-Consistent Approximation](https://mlsanity.com/paper/2407.09687/) (2024)
- [Tuning-free multi-coil compressed sensing MRI with Parallel Variable Density Approximate Message Passing (P-VDAMP)](https://mlsanity.com/paper/2203.04180/) (2022)
- [Sparsity and Coefficient Permutation Based Two-Domain AMP for Image Block Compressed Sensing](https://mlsanity.com/paper/2305.12986/) (2023)
- [A Scalable Training Strategy for Blind Multi-Distribution Noise Removal](https://mlsanity.com/paper/2310.20064/) (2023)

## Abstract (arXiv)

Plug and play (P&P) algorithms iteratively apply highly optimized image denoisers to impose priors and solve computational image reconstruction problems, to great effect. However, in general the "effective noise", that is the difference between the true signal and the intermediate solution, within the iterations of P&P algorithms is neither Gaussian nor white. This fact makes existing denoising algorithms suboptimal. In this work, we propose a CNN architecture for removing colored Gaussian noise and combine it with the recently proposed VDAMP algorithm, whose effective noise follows a predictable colored Gaussian distribution. We apply the resulting denoising-based VDAMP (D-VDAMP) algorithm to variable density sampled compressive MRI where it substantially outperforms existing techniques.