Estimation of instrument and noise parameters for inverse problem based on prior diffusion model

2026-02-13 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, extended

Summary

This article introduces a novel method for estimating observation parameters, specifically instrument response and noise characteristics, within inverse problems where a Bayesian framework and diffusion process prior are used. The approach leverages the G-DSP algorithm, which simplifies posterior sampling and enables the definition of an optimal estimator for both the observation parameters (e.g., Lorentz Point Spread Function width, noise mean, and variance) and the image of interest. The methodology also quantifies uncertainty effectively. Utilizing Markov Chain Monte Carlo (MCMC) algorithms, the system efficiently computes estimates and posterior properties. Numerical experiments, including a toy problem based on the MNIST dataset, confirm the computational efficiency and high quality of both the estimates and uncertainty quantification, demonstrating significant reductions in blur and noise in restored images.

Key takeaway

For research scientists working on inverse problems with diffusion priors, this method offers a robust solution for simultaneously estimating instrument and noise parameters alongside the image of interest. You should consider integrating this Gibbs-Diffusion Posterior Sampling (G-DPS) approach to achieve accurate parameter estimations and reliable uncertainty quantification, especially when dealing with complex observation models and unknown system characteristics. This can lead to significantly improved image restoration and more trustworthy results.

Key insights

A Gibbs-Diffusion Posterior Sampling (G-DPS) based method efficiently estimates observation parameters and images in inverse problems with diffusion priors.

Principles

• Conjugate priors simplify conditional posterior sampling.
• Hierarchical models enable computational simplifications.
• MCMC algorithms provide robust uncertainty quantification.

Method

The proposed method uses a Gibbs loop to iteratively sample each observation parameter and image under its conditional posterior, leveraging the G-DPS algorithm for image sampling and direct sampling for conjugate priors.

In practice

• Apply to inverse problems with unknown instrument response.
• Use for image restoration requiring noise parameter estimation.
• Quantify uncertainty in estimated parameters and images.

Topics

• Inverse Problems
• Diffusion Models
• Bayesian Parameter Estimation
• Markov Chain Monte Carlo
• Image Restoration

Best for: Research Scientist, AI Researcher, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.