1,701 research outputs found
Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imaging
Unsupervised deep learning approaches have recently become one of the crucial
research areas in imaging owing to their ability to learn expressive and
powerful reconstruction operators even when paired high-quality training data
is scarcely available. In this chapter, we review theoretically principled
unsupervised learning schemes for solving imaging inverse problems, with a
particular focus on methods rooted in optimal transport and convex analysis. We
begin by reviewing the optimal transport-based unsupervised approaches such as
the cycle-consistency-based models and learned adversarial regularization
methods, which have clear probabilistic interpretations. Subsequently, we give
an overview of a recent line of works on provably convergent learned
optimization algorithms applied to accelerate the solution of imaging inverse
problems, alongside their dedicated unsupervised training schemes. We also
survey a number of provably convergent plug-and-play algorithms (based on
gradient-step deep denoisers), which are among the most important and widely
applied unsupervised approaches for imaging problems. At the end of this
survey, we provide an overview of a few related unsupervised learning
frameworks that complement our focused schemes. Together with a detailed
survey, we provide an overview of the key mathematical results that underlie
the methods reviewed in the chapter to keep our discussion self-contained
Meta-Prior: Meta learning for Adaptive Inverse Problem Solvers
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
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