标题： 基于能量的逆成像模型 显示英文标题

标题： Energy-based models for inverse imaging problems

摘要： 本章我们全面概述了在逆成像问题背景下使用能量模型（EBMs）的情况。 EBMs 是通过适当的能量泛函 $E$建模的 Gibbs 密度 $p(x) \propto \exp{-E(x)}$概率分布。 在本章中，我们介绍了贝叶斯逆问题的严格理论，包括有限维和无限维设置下的适定性和稳定性结果。 随后我们讨论了 EBMs 在贝叶斯逆问题中的使用，并解释了从数据中学习 EBMs 的最相关技术。 作为贝叶斯逆问题的关键部分，我们涵盖了几种用于从 EBMs 中采样的流行算法，即 Metropolis-Hastings 算法、Gibbs 抽样、Langevin 蒙特卡洛和哈密顿蒙特卡洛。 此外，我们展示了通过利用允许显式验证有效能量模型所需属性的 EBM 解决多个逆成像问题的数值结果。 显示英文摘要

摘要： In this chapter we provide a thorough overview of the use of energy-based models (EBMs) in the context of inverse imaging problems. EBMs are probability distributions modeled via Gibbs densities $p(x) \propto \exp{-E(x)}$ with an appropriate energy functional $E$. Within this chapter we present a rigorous theoretical introduction to Bayesian inverse problems that includes results on well-posedness and stability in the finite-dimensional and infinite-dimensional setting. Afterwards we discuss the use of EBMs for Bayesian inverse problems and explain the most relevant techniques for learning EBMs from data. As a crucial part of Bayesian inverse problems, we cover several popular algorithms for sampling from EBMs, namely the Metropolis-Hastings algorithm, Gibbs sampling, Langevin Monte Carlo, and Hamiltonian Monte Carlo. Moreover, we present numerical results for the resolution of several inverse imaging problems obtained by leveraging an EBM that allows for the explicit verification of those properties that are needed for valid energy-based modeling.