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Minimax Theory of Image Reconstruction

  • Book
  • © 1993

Overview

Authors:
  1. A. P. Korostelev

    1. Institute for Systems Studies, Moscow, Russia

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    You can also search for this author in PubMed   Google Scholar

  2. A. B. Tsybakov

    1. Institute for Problems of Information Transmission, Moscow GSP-4, Russia

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    You can also search for this author in PubMed   Google Scholar

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

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xi
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  2. Nonparametric Regression and Change-Point Problems

    • A. P. Korostelev, A. B. Tsybakov
    Pages 1-45

  3. Minimax Lower Bounds

    • A. P. Korostelev, A. B. Tsybakov
    Pages 46-87

  4. The Problem of Edge and Image Estimation

    • A. P. Korostelev, A. B. Tsybakov
    Pages 88-106

  5. Optimal Image and Edge Estimation for Boundary Fragments

    • A. P. Korostelev, A. B. Tsybakov
    Pages 107-127

  6. Generalizations and Extensions

    • A. P. Korostelev, A. B. Tsybakov
    Pages 128-162

  7. Image Reconstruction Under Restrictions on Estimates

    • A. P. Korostelev, A. B. Tsybakov
    Pages 163-181

  8. Estimation of Support of a Density

    • A. P. Korostelev, A. B. Tsybakov
    Pages 182-197

  9. Estimation of the Domain’s Area

    • A. P. Korostelev, A. B. Tsybakov
    Pages 198-222

  10. Image Estimation from Indirect Observations

    • A. P. Korostelev, A. B. Tsybakov
    Pages 223-242

  11. Back Matter

    Pages 243-260
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Keywords

About this book

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.

Authors and Affiliations

  • Institute for Systems Studies, Moscow, Russia

    A. P. Korostelev

  • Institute for Problems of Information Transmission, Moscow GSP-4, Russia

    A. B. Tsybakov

Bibliographic Information

  • Book Title: Minimax Theory of Image Reconstruction

  • Authors: A. P. Korostelev, A. B. Tsybakov

  • Series Title: Lecture Notes in Statistics

  • DOI: https://doi.org/10.1007/978-1-4612-2712-0

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1993

  • Softcover ISBN: 978-0-387-94028-1Published: 16 April 1993

  • eBook ISBN: 978-1-4612-2712-0Published: 06 December 2012

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 1

  • Number of Pages: XII, 258

  • Topics: Statistics, general

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