Foveal detection and approximation for singularities

✍ Scribed by Stéphane Mallat

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 474 KB
• Volume: 14
• Category: Article
• ISSN: 1063-5203
• DOI: 10.1016/s1063-5203(03)00021-6

✦ Synopsis

Projections in a foveal space at u approximate functions with a resolution that decreases proportionally to the distance from u. Such spaces are defined by dilating a finite family of foveal wavelets, which are not translated. Their general properties are studied and illustrated with spline functions. Orthogonal bases are constructed with foveal wavelets of compact support and high regularity. Foveal wavelet coefficients give pointwise characterization of nonoscillatory singularities. An algorithm to detect singularities and choose foveal points is derived. Precise approximations of piecewise regular functions are obtained with foveal approximations centered at singularity locations.