Inhaltsangabe
Image processing is an increasingly important area of research and there exists a large variety of image reconstruction methods proposed by different authors. This book is concerned with a technique for image reconstruction known as the asymptotic minimax approach, which is based on non-parametric regression and non-parametric change-point analysis. In effect, the central idea is to assume that the image under analysis belongs to a certain functional class and the method finds the image estimators which achieve the best order of accuracy for the worst images in that class. The first two chapters present the basic ideas required from non-parametric regression and change-point analysis whilst the subsequent chapters develop the main theory and examples of applications. In order to provide a relatively simple account of this method, the authors' emphasis is to present results under the simplest assumptions which still allow the main features of a particular problem. As a result the book is essentially self-contained, although it does assume a firm grounding in functional analysis, statistics and image processing fundamentals.
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