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Title: Exponential B-Splines: Scale-Space and Wavelet Representations
Keywords: Exponential B-splines, scale-space, wavelet transform
Issue Date: 2-Aug-2012
Citation: LOR CHOON YEE (2012-08-02). Exponential B-Splines: Scale-Space and Wavelet Representations. ScholarBank@NUS Repository.
Abstract: Exponential B-splines have been well studied in the context of interpolation and approximation theory as a generalization of the classical polynomial B-splines. The focus of this thesis is on two new aspects, namely the scale-space and wavelet representations by exponential B-splines. First, the concept of elementary symmetric polynomials is introduced in order to express derivatives of exponential B-spline in terms of lower order ones. An exponential B-spline is known to satisfy a refinement equation. This property is utilized to formulate the exponential B-spline scale-space representation at rational scale. A simple algorithm for scale-space computation is presented together with some numerical examples. This algorithm can be modified for computation of wavelet transforms defined by derivatives of exponential B-splines. Finally, a semi-discrete wavelet representation for the difference of exponential B-spline scale-space at two consecutive dyadic scales is analyzed.
Appears in Collections:Master's Theses (Open)

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