Wavelet Bases Made of Piecewise Polynomial Functions: Theory and Applications

• 作者: Francesco Zirilli Lorella Fatone Maria Cristina Recchioni
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: APPROXIMATION THEORY WAVELET BASES KERNEL Sparsification Image Compression
• 年，卷（期）: 2011,（2）
• 页码范围: 196-216
• 页数: 21页
• 分类号: O1

摘要

We present wavelet bases made of piecewise (low degree) polynomial functions with an (arbitrary) assigned number of vanishing moments. We study some of the properties of these wavelet bases;in particular we consider their use in the approximation of functions and in numerical quadrature. We focus on two applications: integral kernel sparsification and digital image compression and reconstruction. In these application areas the use of these wavelet bases gives very satisfactory results.