Ten Lectures on WaveletsSIAM, 01/06/1992 - 376 من الصفحات This monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMS-NSF Conference on Wavelets and Applications. Wavelets are a mathematical development that many experts think may revolutionize the world of information storage and retrieval. They are a fairly simple mathematical tool now being applied to the compression of data, such as fingerprints, weather satellite photographs, and medical x-rays - that were previously thought to be impossible to condense without losing crucial details. The opening chapter provides an overview of the main problems presented in the book. Following chapters discuss the theoretical and practical aspects of wavelet theory, including wavelet transforms, orthonormal bases of wavelets, and characterization of functional spaces by means of wavelets. The last chapter presents several topics under active research, as multidimensional wavelets, wavelet packet bases, and a construction of wavelets tailored to decompose functions defined in a finite interval. |
المحتوى
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CB61_backmatter | 341 |
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عبارات ومصطلحات مألوفة
algorithm applications biorthogonal Chapter choice choose coiflet compact compactly supported compactly supported wavelets compute constitute a frame constitute an orthonormal construction continuous wavelet transform convergence corresponding defined dilation factor dx f(x dyadic rationals eigenvalues equivalent example exists exponential decay Figure finite follows formula Fourier transform frame bounds frequency function ƒ ƒ dx gm,n gw,t Haar basis hence Hilbert space Hölder continuous implies integral L²(R leads Lemma linear m₁ Meyer multiresolution analysis N₁ operator orthogonal orthonormal basis orthonormal wavelet bases plots proof prove Ran F reconstruction refinement scheme regularity Riesz Riesz basis satisfies scaling function sequence sin² spline subband filtering subspace support width symmetric theorem tight frame time-frequency localization trigonometric polynomial Twav values vanishing moments wavelet transform windowed Fourier transform woto zero Σ Σ ωο