Ten Lectures on Wavelets
Wavelets are a mathematical development that may revolutionize the world of information storage and retrieval according to many experts. 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. This monograph contains 10 lectures presented by Dr. Daubechies as the principal speaker at the 1990 CBMS-NSF Conference on Wavelets and Applications. The author has worked on several aspects of the wavelet transform and has developed a collection of wavelets that are remarkably efficient.
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already apply approximation argument associated assume Banach spaces bounded called Chapter choice choose close coefficients compact compactly supported completely compute Consequently constant constitute construction continuous convergence corresponding Daubechies decay deﬁned derivative dilation discrete eigenvalues equal equation equivalent estimates example exists fact factor Figure ﬁlter ﬁnd ﬁnite ﬁrst follows formula Fourier transform frame frequency function given gives Haar hand hence holds implies independent integral leads Lemma limit linear localization means method Meyer Moreover multiresolution analysis Note obtained operator orthogonal orthonormal basis orthonormal wavelet particular phase plots positive possible practice proof properties Proposition prove reconstruction regularity requirement respect restrict result satisﬁes satisfy scaling scheme sequence shows similar space Suppose symmetric theorem time-frequency values wavelet bases wavelet transform windowed Fourier zero