Pre-wavelets and image compression
Abstract
We study the compression of two dimensional digitized images by means of pre-wavelet transforms. First, we review some of the properties of wavelets. Then we construct a basis of piecewise linear pre-wavelets. We decompose functions in certain Besov spaces into a linear combination of these pre-wavelets and prove that the error introduced by using only a finite number of coefficients is bounded in terms of the number of nonzero coefficients and in terms of the Besov space norm of the image function. We describe a computer algorithm that performs such a decomposition and then report on the results of numerical experiments.
Degree
Ph.D.
Advisors
Lucier, Purdue University.
Subject Area
Mathematics
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