Spline Interpolation and Wavelet Construction
Copyright policy )Spline Interpolation and Wavelet Construction
The method of Dubuc and Deslauriers on symmetric interpolatory subdivision is extended to study the relationship between interpolation processes and wavelet construction. Refinable and interpolatory functions are constructed in stages from \(B\)-splines. Their method constructs the filter sequence (its Laurent polynomial) of the interpolatory function as a product of Laurent polynomials. This provides a natural way of splitting the filter for the construction of orthonormal and biorthogonal scaling functions leading to orthonormal and biorthogonal wavelets. Their method also leads to a class of filters which includes the minimal length Daubechies compactly supported orthonormal wavelet coefficients. Examples of ``good'' filters are given, together with results of numerical experiments conducted to test the performance of these filters in data compression.
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cascade algorithm, interpolatory function, Nontrigonometric harmonic analysis involving wavelets and other special systems, Wavelets, orthonormal basis, wavelets, 510, Refinable function, Condition E, Cascade algorithm, Biorthogonal basis, Uniform B-spline, Applied Mathematics, Orthonormal basis, Subdivision algorithm, subdivision algorithm, uniformB-spline, Riesz basis, transition operator, Spline approximation, Euler-Frobenius polynomial, refinable function, uniform B-spline, Transition operator, Interpolatory function, biorthogonal basis, Euler–Frobenius polynomial
cascade algorithm, interpolatory function, Nontrigonometric harmonic analysis involving wavelets and other special systems, Wavelets, orthonormal basis, wavelets, 510, Refinable function, Condition E, Cascade algorithm, Biorthogonal basis, Uniform B-spline, Applied Mathematics, Orthonormal basis, Subdivision algorithm, subdivision algorithm, uniformB-spline, Riesz basis, transition operator, Spline approximation, Euler-Frobenius polynomial, refinable function, uniform B-spline, Transition operator, Interpolatory function, biorthogonal basis, Euler–Frobenius polynomial
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