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Books > Computing & IT > Applications of computing > Image processing
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Minimax Theory of Image Reconstruction (Paperback, Softcover reprint of the original 1st ed. 1993)
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Minimax Theory of Image Reconstruction (Paperback, Softcover reprint of the original 1st ed. 1993)
Series: Lecture Notes in Statistics, 82
Expected to ship within 10 - 15 working days
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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.
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