Meta-Prior: Meta learning for Adaptive Inverse Problem Solvers

TL;DR

This paper introduces a meta-learning approach for inverse imaging problems that enables quick adaptation to new tasks with minimal data, extending to unsupervised settings and achieving near-optimal performance.

Contribution

The paper presents a novel meta-learning framework for inverse problems that works with supervised and unsupervised data, allowing efficient task adaptation and generalization.

Findings

Recovers Bayes optimal estimator in simple settings

Effective on image processing and MRI tasks

Works with limited ground truth data

Abstract

Deep neural networks have become a foundational tool for addressing imaging inverse problems. They are typically trained for a specific task, with a supervised loss to learn a mapping from the observations to the image to recover. However, real-world imaging challenges often lack ground truth data, rendering traditional supervised approaches ineffective. Moreover, for each new imaging task, a new model needs to be trained from scratch, wasting time and resources. To overcome these limitations, we introduce a novel approach based on meta-learning. Our method trains a meta-model on a diverse set of imaging tasks that allows the model to be efficiently fine-tuned for specific tasks with few fine-tuning steps. We show that the proposed method extends to the unsupervised setting, where no ground truth data is available. In its bilevel formulation, the outer level uses a supervised loss, that evaluates how well the fine-tuned model performs, while the inner loss can be either supervised or unsupervised, relying only on the measurement operator. This allows the meta-model to leverage a few ground truth samples for each task while being able to generalize to new imaging tasks. We show that in simple settings, this approach recovers the Bayes optimal estimator, illustrating the soundness of our approach. We also demonstrate our method's effectiveness on various tasks, including image processing and magnetic resonance imaging.