Outlier-Robust Diffusion Solvers for Inverse Problems

TL;DR

This paper introduces outlier-robust diffusion-based solvers for inverse problems, combining noise estimation, Huber loss, and advanced optimization techniques to improve robustness and performance.

Contribution

It develops a novel framework integrating explicit noise estimation and reweighted least squares with gradient and conjugate gradient methods for robustness against outliers.

Findings

Our methods outperform recent diffusion model-based approaches in robustness.

The proposed approach effectively mitigates outlier effects in various inverse problems.

Experiments show improved accuracy across multiple datasets and conditions.

Abstract

Methods based on diffusion models (DMs) for solving inverse problems (IPs) have recently achieved remarkable performance. However, DM-based methods typically struggle against outliers, which are common in real-world measurements. In this work, to tackle IPs with outliers, we first refine the measurement via explicit noise estimation to mitigate the effect of noise. Subsequently, we formulate an iteratively reweighted least squares objective based on the Huber loss to address the outliers. We propose a method utilizing gradient descent to approximately solve the corresponding optimization problem for the robust objective. To avoid delicate tuning of the learning rate required by the gradient descent method, we further employ the conjugate gradient method with an efficient strategy for updating. Extensive experiments on multiple image datasets for linear and nonlinear tasks under various conditions demonstrate that our proposed methods exhibit robustness to outliers and outperform recent DM-based methods in most cases.