本文为意大利特伦托大学（作者：Massimo Zanetti）的博士论文，共198页。

新一代遥感卫星的多光谱图像越来越多，为地球观测和监测提供了前所未有的信息来源。现在，多光谱图像可以以高分辨率（几乎）覆盖所有陆地表面，而且回访时间极短（最多几天），这使得绘制全球变化图成为可能。从如此庞大的数据中提取有用的信息需要在几乎所有的应用环境中系统地使用自动技术。在某些情况下，严格的应用要求迫使实践者在处理链的研究中开发强大的数据驱动方法。因此，所采用的理论模型与求解的物理意义之间的确切关系有时隐藏在数据分析技术中，或者根本不清楚。尽管这并不是应用程序本身成功的限制，但它使得从一个特定问题学到的知识很难转移到另一个问题。

本文主要针对这一问题，提出了多光谱图像表示与分析的一般数学框架。然后将所提出的模型应用于变化检测的应用环境中。这里所提出模型的普遍性使我们能够：（1）对现有的变化检测方法提供数学解释，并且（2）将它们扩展到更一般的情况，以解决日益复杂的问题。上一代多光谱图像的典型空间/光谱特性强调了需要有更灵活的模型来表示图像。事实上，在前几代多光谱图像上运行良好的经典变化检测方法，由于其对上一代产品中所有复杂光谱/空间细节的建模能力较差，只是提供了次优结果。本文提出的理论模型旨在为图像的表示提供更多的自由度。通过对合成数据集和真实多光谱图像的实验，证明了所提出的新方法和相关技术的有效性。这里所采用模型的改进灵活性允许更好地表示数据，并使变化检测性能得到实质性改进。

The increasing availability of newgeneration remote sensing satellite multispectral images provides anunprecedented source of information for Earth observation and monitoring.Multispectral images can be now collected at high resolution covering (almost)all land surfaces with extremely short revisit time (up to a few days), makingit possible the mapping of global changes. Extracting useful information fromsuch huge amount of data requires a systematic use of automatic techiques inalmost all applicative contexts. In some cases, the strict applicationrequirements force the pratictioner to develop strongly data-driven approachesin the development of the processing chain. As a consequence, the exactrelationship between the theoretical models adopted and the physical meaning ofthe solutions is sometimes hidden in the data analysis techniques, or not clearat all. Altough this is not a limitation for the success of the applicationitself, it makes however difficult to transfer the knowledge learned from onespecific problem to another. In this thesis we mainly focus on this aspect andwe propose a general mathematical framework for the representation and analysisof multispectral images. The proposed models are then used in the applicativecontext of change detection. Here, the generality of the proposed models allowsus to both: (1) provide a mathematical explanation of already existingmethodologies for change detection, and (2) extend them to more general casesfor addressing problems of increasing complexity. Typical spatial/spectralproperties of last generation multispectral images emphasize the need of havingmore flexible models to image representation. In fact, classical methods tochange detection that have worked well on previous generations of multispectralimages provide sub-optimal results due to their poor capability of modeling allthe complex spectral/spatial detail available in last generation products. Thetheoretical models presented in this thesis are aimed at giving more degrees offreedom in the representation of the images. The effectiveness of the proposednovel approaches and related techniques is demonstrated on several experimentsinvolving both synthetic datasets and real multispectral images. Here, theimproved flexibility of the models adopted allows for a better representationof the data and is always followed by a substantial improvement of the changedetection performance.

1. 引言

2. 项目背景

3. 变分泛函图像逼近的数值最小化

4. 向量值图像和曲线的变分逼近

5. 背景介绍

6. 用于二元变化检测的Rayleigh-Rice混合模型

7. 一种用于变化检测的复合多类混合模型

8. 基于自由间断模型的多光谱图像变化检测的类空间上下文方法

9. 结论与未来展望

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