A large number of imaging problems reduce to the optimization of a cost function, with typical structural properties. The aim of this paper is to describe the state of the art in continuous optimization methods for such problems, and present the most successful approaches and their interconnections. We place particular emphasis on optimal first-order schemes that can deal with typical non-smooth and large-scale objective functions used in imaging problems. We illustrate and compare the different algorithms using classical non-smooth problems in imaging, such as denoising and deblurring. Moreover, we present applications of the algorithms to more advanced problems, such as magnetic resonance imaging, multilabel image segmentation, optical flow estimation, stereo matching, and classification.

中文翻译：

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成像持续优化简介

大量的成像问题归结为具有典型结构特性的成本函数的优化。本文的目的是描述针对此类问题的持续优化方法的最新技术，并介绍最成功的方法及其相互联系。我们特别强调可以处理成像问题中使用的典型非光滑和大规模目标函数的最佳一阶方案。我们使用成像中的经典非平滑问题来说明和比较不同的算法，例如去噪和去模糊。此外，我们将算法应用于更高级的问题，例如磁共振成像、多标签图像分割、光流估计、立体匹配和分类。