论文信息 - Orthonormal RBF Wavelet and Ridgelet-like Series and Transforms for High- Dimensional Problems

Orthonormal RBF Wavelet and Ridgelet-like Series and Transforms for High- Dimensional Problems

This paper developed a systematic strategy establishing RBF on the wavelet analysis, which includes continuous and discrete RBF orthonormal wavelet transforms respectively in terms of singular fundamental solutions and nonsingular general solutions of differential operators. In particular, the harmonic Bessel RBF transforms were presented for high-dimensional data processing. It was also found that the kernel functions of convection-diffusion operator are feasible to construct some stable ridgelet-like RBF transforms. We presented time-space RBF transforms based on non-singular solution and fundamental solution of time-dependent differential operators. The present methodology was further extended to analysis of some known RBFs such as the MQ, Gaussian and pre-wavelet kernel RBFs.

W. Chen | W. Chen

[1] R. Schaback,et al. Numerical Techniques Based on Radial Basis Functions , 2000 .

[2] Wen Chen,et al. Relationship between boundary integral equation and radial basis function , 2002, ArXiv.

[3] Charles K. Chui,et al. Analytic wavelets generated by radial functions , 1996, Adv. Comput. Math..

[4] C. Chui. Wavelets: A Mathematical Tool for Signal Analysis , 1997 .

[5] Gregory Piatetsky-Shapiro,et al. High-Dimensional Data Analysis: The Curses and Blessings of Dimensionality , 2000 .

[6] W. Chen,et al. A note on radial basis function computing , 2001, ArXiv.

[7] Dean G. Duffy,et al. Transform Methods for Solving Partial Differential Equations , 2004 .

[8] L. Schumaker,et al. Scattered data fitting on the sphere , 1998 .

[9] Wen Chen,et al. New Insights in Boundary-only and Domain-type RBF Methods , 2002, ArXiv.

[10] E. Candès,et al. Ridgelets: a key to higher-dimensional intermittency? , 1999, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.