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Minimax Theory of Image Reconstruction

  • A. P. Korostelev
  • A. B. Tsybakov

Part of the Lecture Notes in Statistics book series (LNS, volume 82)

Table of contents

  1. Front Matter
    Pages i-xi
  2. A. P. Korostelev, A. B. Tsybakov
    Pages 1-45
  3. A. P. Korostelev, A. B. Tsybakov
    Pages 46-87
  4. A. P. Korostelev, A. B. Tsybakov
    Pages 88-106
  5. A. P. Korostelev, A. B. Tsybakov
    Pages 107-127
  6. A. P. Korostelev, A. B. Tsybakov
    Pages 128-162
  7. A. P. Korostelev, A. B. Tsybakov
    Pages 163-181
  8. A. P. Korostelev, A. B. Tsybakov
    Pages 182-197
  9. A. P. Korostelev, A. B. Tsybakov
    Pages 198-222
  10. A. P. Korostelev, A. B. Tsybakov
    Pages 223-242
  11. Back Matter
    Pages 243-260

About this book

Introduction

There exists a large variety of image reconstruction methods proposed by different authors (see e. g. Pratt (1978), Rosenfeld and Kak (1982), Marr (1982)). Selection of an appropriate method for a specific problem in image analysis has been always considered as an art. How to find the image reconstruction method which is optimal in some sense? In this book we give an answer to this question using the asymptotic minimax approach in the spirit of Ibragimov and Khasminskii (1980a,b, 1981, 1982), Bretagnolle and Huber (1979), Stone (1980, 1982). We assume that the image belongs to a certain functional class and we find the image estimators that achieve the best order of accuracy for the worst images in the class. This concept of optimality is rather rough since only the order of accuracy is optimized. However, it is useful for comparing various image reconstruction methods. For example, we show that some popular methods such as simple linewise processing and linear estimation are not optimal for images with sharp edges. Note that discontinuity of images is an important specific feature appearing in most practical situations where one has to distinguish between the "image domain" and the "background" . The approach of this book is based on generalization of nonparametric regression and nonparametric change-point techniques. We discuss these two basic problems in Chapter 1. Chapter 2 is devoted to minimax lower bounds for arbitrary estimators in general statistical models.

Keywords

estimator image analysis likelihood statistical model

Authors and affiliations

  • A. P. Korostelev
    • 1
  • A. B. Tsybakov
    • 2
  1. 1.Institute for Systems StudiesMoscowRussia
  2. 2.Institute for Problems of Information TransmissionMoscow GSP-4Russia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-2712-0
  • Copyright Information Springer-Verlag New York 1993
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94028-1
  • Online ISBN 978-1-4612-2712-0
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site
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