Polyharmonic Smoothing Splines for Multi-Dimensional Signals with 1/W - Like Spectra

Abstract

Motivated by the fractal-like behavior of natural images, we propose a new smoothing technique that uses a regularization functional which is a fractional iterate of the Laplacian. This type of functional has previously been introduced by Duchon in the context of radial basis functions (RBFs) for the approximation of non-uniform data. Here, we introduce a new solution to Duchon's smoothing problem in multiple dimensions using non-separable fractional polyharmonic B-splines. The smoothing is performed in the Fourier domain by filtering, thereby making the algorithm fast enough for most multi-dimensional real-time applications.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jan 07, 2005
Accession Number
ADA433580

Entities

People

  • Dimitri Van De Ville
  • Michael Unser
  • Shai Tirosh

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Electronic Mail
  • Filtration
  • Frequency
  • Frequency Domain
  • Frequency Response
  • Functional Analysis
  • Information Operations
  • Mathematics
  • Polynomials
  • Sequences
  • Signal Processing
  • Spectra
  • Statistics

Readers

  • Approximation Theory.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)