Meta-Prior: Meta learning for Adaptive Inverse Problem Solvers

Matthieu Terris, Thomas Moreau

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Keywords: Meta learning, inverse problems, imaging, self supervised learning

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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, such that it can be adapted to specific tasks with a few steps of fine-tuning. The outer level uses a supervised loss, that evaluates how well the fine-tuned model performs, while the inner loss can be 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 imaging tasks, including image processing and magnetic resonance imaging.

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Submission Number: 5161