Digital Image Restoration Under a Regression Model - The Unconstrained, Linear Equality and Inequality Constrained Approaches

Abstract

The problem of restoring images degraded by blur and corrupted by noise is considered in this report. A discretization of the Fredholm integral equation of the first kind in a two dimensional form is performed. The overdetermined and underdetermined regression models are examined in detail, with particular attention to the problem of ill conditioning. The results of the restoration of simulated pictures under atmospheric turbulence and diffraction limited point spread functions are presented. A priori information in the form of deterministic constraints is proposed as a means to solve the ill conditioning problem. With linear equality constraints, a combination of estimation and hypothesis testing is used to decide if a reduction of the mean square error occurs upon the imposition of the restrictions. Experimental results show that more acceptable results are obtained in the restoration. Linear inequality constraints are incorporated by a quadratic programming formulation. The use of low (nonnegativeness) and upper bounds indicate a substantial improvement in the restoration, even for the ill conditioned situation.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1974
Accession Number
ADA034742

Entities

People

  • Nelson Delfino D'avila Mascarenhas

Organizations

  • University of Southern California

Tags

Communities of Interest

  • Advanced Electronics
  • Air Platforms
  • Energy and Power Technologies
  • Space

DTIC Thesaurus Topics

  • Algorithms
  • Atmospheric Motion
  • Computational Science
  • Data Science
  • Equations
  • Estimators
  • Geometry
  • Image Processing
  • Information Processing
  • Information Science
  • Integral Equations
  • Integrals
  • Linear Programming
  • Mathematical Filters
  • Mathematical Models
  • Statistical Algorithms
  • Statistical Analysis

Readers

  • Calculus or Mathematical Analysis
  • Image Processing and Computer Vision.
  • Operations Research