SPLINE INTERPOLATION AND WAVELET CONSTRUCTION

The method of Dubuc and Deslauriers on symmetric interpolatory subdivi sion is extended to study the relationship between interpolation proce sses and wavelet construction. Refinable and interpolatory functions a re constructed in stages from B-splines. Their method constructs the f ilter sequence (its Laurent polynomial) of the interpolatory function as a product of Laurent polynomials. This provides a natural way of sp litting the filter for the construction of orthonormal and biorthogona l scaling functions leading to orthonormal and biorthogonal wavelets. Their method also leads to a class of filters which includes the minim al length Daubechies compactly supported orthonormal wavelet coefficie nts. Examples of ''good'' filters are given together with results of n umerical experiments conducted to test the performance of these filter s in data compression. (C) 1998 Academic Press.