图像处理中的数学问题（英文版）

偏微分方程和变分法用于图像处理始于15年前，从此人们一直在研究相关理论。本书向读者介绍了图像应用及相关的数学知识，本书自成一体，主要面向两类读者，一类是数学专业人士，从中他们可以了解数学对于图像处理领域的贡献，从而更致力于研究一些尚未解决的问题；另一类是计算机视觉领域人士，从中可以学到与图像处理有关数学理论。
目次：导论；数学基础理论；图像恢复；分段问题；应用问题；有限微分法导论。
读者对象：数学及计算机视觉专业的研究人员及研究生。

偏微分方程和变分法用于图像处理始于15年前，从此人们一直在研究相关理论。本书向读者介绍了图像应用及相关的数学知识，本书自成一体，主要面向两类读者，一类是数学专业人士，从中他们可以了解数学对于图像处理领域的贡献，从而更致力于研究一些尚未解决的问题；另一类是计算机视觉领域人士，从中可以学到与图像处理有关数学理论。

Foreword
Preface
Guide to the Main Mathematical Concepts and
Their Application
Notation and Symbols
Introduction
1.1 The Image Society
1.2 What Is a Digital Image?
1.3 About Partial Differential Equations (PDEs)
1.4 Detailed Plan
Mathematical Preliminaries
How to Read This Chapter
2.1 The Direct Method in the Calculus of Variations
2.1.1 Topologies on Banach Spaces
2.1.2 Convexity and Lower Semicontinuity
2.1.3 Relaxation
2.1.4 About F-Convergence
2.2 The Space of Functions of Bounded Variation
2.2.1 Basic Definitions on Measures

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