  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.
