Locating and Correcting Errors in Images (1997)
BibTeX
@MISC{Jos'e97locatingand,
author = {Paulo Ferreira Jos'e and Paulo J. S. G. Ferreira and Jos'e M. N. Vieira},
title = {Locating and Correcting Errors in Images},
year = {1997}
}
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Abstract
Most image interpolation or extrapolation algorithms assume that the locations of the unknown pixels are known. In this paper we attempt to remove this restriction. More precisely, we propose an algorithm for locating the incorrect pixels of an image, assuming only partial knowledge of its Fourier transform. Note that this is a nonlinear problem: the unknown quantities are the positions and values of the (say) n erroneous pixels. We show that the positions can be evaluated in O(n 2 ) or even O(n log n) flops by solving a set of n linear equations and computing a FFT. The determination of n is part of the algorithm, whose stability is also briefly discussed. The values of the n incorrect pixels can then be estimated using any of the interpolation methods known. 1 Notation The complex N-dimensional space, with the usual inner product and norm, is denoted by C N . The conjugate transpose is denoted by . The Fourier matrix F is the unitary N \Theta N matrix whose elements F ab are gi...
Keyphrases
incorrect pixel nonlinear problem unknown pixel fourier transform partial knowledge linear equation unknown quantity extrapolation algorithm unitary theta matrix interpolation method element ab usual inner product erroneous pixel image interpolation fourier matrix complex n-dimensional space conjugate transpose
