Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview

Alexander Auras; Kanchana Vaishnavi Gandikota; Hannah Droege; Michael Moeller

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arXiv · 2402.12072

Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview

Alexander Auras·Kanchana Vaishnavi Gandikota·Hannah Droege·Michael Moeller

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Abstract

This paper provides an overview of current approaches for solving inverse problems in imaging using variational methods and machine learning. A special focus lies on point estimators and their robustness against adversarial perturbations. In this context results of numerical experiments for a one-dimensional toy problem are provided, showing the robustness of different approaches and empirically verifying theoretical guarantees. Another focus of this review is the exploration of the subspace of data-consistent solutions through explicit guidance to satisfy specific semantic or textural properties.

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eess.IV cs.CV cs.LG cs.NA math.NA

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Alexander Auras, Kanchana Vaishnavi Gandikota, Hannah Droege, Michael Moeller. 2024-02-19. Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview. https://arxiv.org/abs/2402.12072

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