# Adaptive Sampling for Linear Sensing Systems via Langevin Dynamics

## TL;DR

This paper introduces a Bayesian adaptive sampling method using Langevin dynamics to improve image quality and speed in sensing systems, demonstrated on MRI with significant quality gains.

## Contribution

It presents a novel Bayesian adaptive sampling approach based on SGLD that generalizes well across different image priors and out-of-distribution data.

## Key findings

- Improved MRI image quality by 2-3 dB PSNR.
- Effective adaptive sampling enhances subtle detail restoration.
- Method generalizes across analytical and neural network priors.

## Abstract

Adaptive or dynamic signal sampling in sensing systems can adapt subsequent sampling strategies based on acquired signals, thereby potentially improving image quality and speed. This paper proposes a Bayesian method for adaptive sampling based on greedy variance reduction and stochastic gradient Langevin dynamics (SGLD). The image priors involved can be either analytical or neural network-based. Notably, the learned image priors generalize well to out-of-distribution test cases that have different statistics than the training dataset. As a real-world validation, the method is applied to accelerate the acquisition of magnetic resonance imaging (MRI). Compared to non-adaptive sampling, the proposed method effectively improved the image quality by 2-3 dB in PSNR, and improved the restoration of subtle details.