A Note on the Daubechies Approach in the Construction of Spline Type Orthogonal Scaling Functions

2015/07/11 by Tian-Xiao He, He, Tian-Xiao, Tung Nguyen +1
Computer Science · Engineering · Mathematics · #Image and Signal Denoising Methods #Advanced Image Fusion Techniques #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.1507.03057

Abstract

We use Lorentz polynomials to present the solutions explicitly of equations (6.1.7) of [I. Daubechies, Ten lectures on wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics, 61. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1992] and (4.9) of [I. Daubechies, Orthonormal bases of compactly supported wavelets. Comm. Pure Appl. Math. 41 (1988), no. 7, 909--996] sot that we give an efficient way to prove Daubechies' results on the existence of spline type orthogonal scaling functions and to evaluate Daubechies scaling functions.

Citations

• Orthonormal bases of compactly supported wavelets

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• Bivariate Daubechies Scaling Functions (Wavelets)
• About construction of orthogonal wavelets with compact support and with scaling coefficient N
• Asymptotics and numerics of zeros of polynomials that are related to Daubechies wavelets
• Regularity of generalized Daubechies wavelets reproducing exponential polynomials
• On the bounds of coefficients of Daubechie's orthonormal wavelets