Statistical Regularization and Learning Theory Lecture : 17 Wavelet Approximation
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چکیده
, where C0 = ∫ 1 0 f(t)dt. j ∼ scale, k ∼ position. Key properties: 1. vanishing moments: We say ψ has M vanishing moments when ∫ 1 0 tψj,k(t)dt = 0 form = 0, 1, . . . ,M− 1 This means the wavelet is “blind” to polynomial segment with degree α ≤M − 1 2. compact support: a daubechies wavelet with M vanishing moments has support ∝ 2M. Together, these properties imply that only O(l log n) nonzero wavelet coefficients are needed to represent a piecewise polynomial function with l pieces and degree α ≤M − 1 on each piece.
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تاریخ انتشار 2004