By Bilusyak N. I., Ptashnyk B. I.
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Additional info for A Boundary-Value Problem for Weakly Nonlinear Hyperbolic Equations with Data on the Entire Boundary of a Domain
Warren. Multiresolution surfaces of arbitrary topological type. Department of Computer Science and Engineering 93-10-05, University of Washington, October 1993. Updated version available as 93-10-05b, January, 1994. 81 M. Lundberg and G. Welland. Construction of compact p-wavelets. Constr. , 9:347 370, 1993. 82 S. Mallat and S. Zhong. Wavelet transform maxima and multiscale edges. In 95 , pages 67 104. 83 S. Mallat and S. Zhong. Characterization of signals from multiscale edges. IEEE Trans. Patt.
Suppose now we know the location of the jumps. If we use interval wavelets on each interval between two jumps, and thus segment the signal accordingly, we would get fast convergence everywhere. Wavelet probing is a technique which allows us to locate the jumps. It simply tries every location between two samples and checks whether it would pay o to segment at this location. g. with the entropy of the wavelet coe cients. Probing one location only requires altering log M coe cients where M is the number of samples.
Finally the author would like to thank the two referees for their thorough reports and for pointing out oversights in the original submission. Their constructive comments have lead to a much improved paper. While conducting this research the author was partially supported by NSF EPSCoR Grant EHR 9108772 and DARPA Grant AFOSR F49620-93-1-0083. He is also on leave as Senior Research Assistant of the National Fund of Scienti c Research Belgium NFWO. References 1 R. Abgral and A. Harten. Multiresolution representation in unstructured meshes.
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