# Efficient Gaussian Sampling for Solving Large-Scale Inverse Problems using MCMC Methods

arXiv: https://arxiv.org/abs/1409.0606 · HTML: https://mlsanity.com/paper/1409.0606/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Sep 2014.

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

- [The split Gibbs sampler revisited: improvements to its algorithmic structure and augmented target distribution](https://mlsanity.com/paper/2206.13894/) (2022)
- [Towards Interpretable Video Super-Resolution via Alternating Optimization](https://mlsanity.com/paper/2207.10765/) (2022)
- [Personalised Federated Learning On Heterogeneous Feature Spaces](https://mlsanity.com/paper/2301.11447/) (2023)

## Abstract (arXiv)

The resolution of many large-scale inverse problems using MCMC methods requires a step of drawing samples from a high dimensional Gaussian distribution. While direct Gaussian sampling techniques, such as those based on Cholesky factorization, induce an excessive numerical complexity and memory requirement, sequential coordinate sampling methods present a low rate of convergence. Based on the reversible jump Markov chain framework, this paper proposes an efficient Gaussian sampling algorithm having a reduced computation cost and memory usage. The main feature of the algorithm is to perform an approximate resolution of a linear system with a truncation level adjusted using a self-tuning adaptive scheme allowing to achieve the minimal computation cost. The connection between this algorithm and some existing strategies is discussed and its efficiency is illustrated on a linear inverse problem of image resolution enhancement.