Deblurring Gaussian Blur.

Abstract

Gaussian blur, or convolution against a Gaussian kernel, is a common model for image and signal degradation. In general, the process of reversing Gaussian blur is unstable, and cannot be represented as a convolution filter in the spatial domain. If we restrict the space of allowable functions to polynomials of fixed finite degree, then a convolution inverse does exist. We give constructive formulas for the deblurring kernels in terms of Hermite polynomials, and observe that their use yields optimal approximate deblurring solutions among the space of bounded degree polynomials. The more common methods of achieving stable approximate deblurring include restrictions to band-limited functions or functions of bounded norm. Keywords: approximate inverse method; heat equation.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1986
Accession Number
ADA178954

Entities

People

  • B. Kimia
  • R. Hummel
  • S. W. Zucker

Organizations

  • New York University

Tags

Communities of Interest

  • Autonomy
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Computer Science
  • Computers
  • Differential Equations
  • Digital Image Processing
  • Digital Images
  • Electrical Engineering
  • Equations
  • Image Processing
  • Images
  • Mathematical Analysis
  • New York
  • Numerical Analysis
  • Partial Differential Equations
  • Pattern Recognition
  • Real Variables
  • Robotics
  • Theorems

Readers

  • Approximation Theory.
  • Ballistic Missile Meteorology
  • Calculus or Mathematical Analysis

Technology Areas

  • Space
  • Space - Space Objects