Mathematical Problems in Imaging, Statistical Mechanics and Related Topics

Abstract

During the duration of this grant I did carry out work on a few loosely related areas, including diffuse tomography, the phase problem in X-ray crystallography, some relations between the Darboux process applied to orthogonal polynomials and the electrostatic interpretation of their zeros, and a number of specific problems related to the bispectral problem. This last one is an area that I initiated about a decade ago starting from a concrete problem in medical imaging. This field has made contact with several unrelated fields in mathematics, ranging from wave propagation, cumulative rings of differential operators, etc. I expect that some of these topics will continue to be of interest to the Air Force, although some of the efforts may have to be redirected. As an example I notice that my initial work on Diffuse Tomography could become of some relevance to work being done at the Air Force Research Laboratory at Kirkland AFB, in the Advanced Optics and Imaging Division by Dr. Charles Matson.

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Document Details

Document Type
Technical Report
Publication Date
Mar 31, 1999
Accession Number
ADA385549

Entities

People

  • F. A. Grunbaum

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Air Force
  • Air Force Research Laboratories
  • Applied Mathematics
  • Concrete
  • Detection
  • Diagnostic Imaging
  • Equations
  • Inverse Problems
  • Materials
  • Mathematics
  • Mechanics
  • Military Research
  • Physics
  • Polynomials
  • Statistical Mechanics
  • Tomography
  • Wave Propagation

Readers

  • Calculus or Mathematical Analysis
  • Image Processing and Computer Vision.
  • Technical Research and Report Writing.