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Proceedings Paper

Case study of nonlinear inverse problems: mammography and nondestructive evaluation
Author(s): Olga Kosheleva; Sergio D. Cabrera; Roberto A. Osegueda; Carlos M. Ferregut; Soheil Nazarian; Debra L. George; Mary J. George; Vladik Kreinovich; Keith Worden
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Paper Abstract

The inverse problem is usually difficult because the signal that we want to reconstruct is weak. Since it is weak, we can usually neglect quadratic and higher order terms, and consider the problem to be linear. Since the problem is linear, methods of solving this problem are also, mainly, linear. In most real-life problems, this linear description works pretty well. However, at some point, when we start looking for a better accuracy, we must take into consideration non-linear terms. This may be a minor improvement for normal image processing, but these non- linear terms may lead to a major improvement and a great enhancement if we are interested in outliers such as faults in non-destructive evaluation or bumps in mammography. Non- linear terms give a great relative push to large outliers, and thus, in these non-linear terms, the effect of irregularities dominate. The presence of the non-linear terms can serve, therefore, as a good indication of the presence of irregularities.

Paper Details

Date Published: 22 September 1998
PDF: 8 pages
Proc. SPIE 3459, Bayesian Inference for Inverse Problems, (22 September 1998); doi: 10.1117/12.323792
Show Author Affiliations
Olga Kosheleva, Univ. of Texas at El Paso] (United States)
Sergio D. Cabrera, Univ. of Texas at El Paso] (United States)
Roberto A. Osegueda, Univ. of Texas at El Paso] (United States)
Carlos M. Ferregut, Univ. of Texas at El Paso] (United States)
Soheil Nazarian, Univ. of Texas at El Paso] (United States)
Debra L. George, Univ. of Texas at El Paso] (United States)
Mary J. George, Univ. of Texas at El Paso] (United States)
Vladik Kreinovich, Univ. of Texas at El Paso] (United States)
Keith Worden, Univ. of Sheffield (United Kingdom)

Published in SPIE Proceedings Vol. 3459:
Bayesian Inference for Inverse Problems
Ali Mohammad-Djafari, Editor(s)

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