Case study of nonlinear inverse problems: mammography and nondestructive evaluation

Olga Kosheleva; Sergio D. Cabrera; Roberto A. Osegueda; Carlos M. Ferregut; Soheil Nazarian; Debra L. George; Mary J. George; Vladik Kreinovich; Keith Worden

doi:10.1117/12.323792

22 September 1998 Case study of nonlinear inverse problems: mammography and nondestructive evaluation

Olga Kosheleva, Sergio D. Cabrera, Roberto A. Osegueda, Carlos M. Ferregut, Soheil Nazarian, Debra L. George, Mary J. George, Vladik Kreinovich, Keith Worden

Author Affiliations +

Proceedings Volume 3459, Bayesian Inference for Inverse Problems; (1998) https://doi.org/10.1117/12.323792
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1998, San Diego, CA, United States

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.

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Olga Kosheleva, Sergio D. Cabrera, Roberto A. Osegueda, Carlos M. Ferregut, Soheil Nazarian, Debra L. George, Mary J. George, Vladik Kreinovich, and Keith Worden "Case study of nonlinear inverse problems: mammography and nondestructive evaluation", Proc. SPIE 3459, Bayesian Inference for Inverse Problems, (22 September 1998); https://doi.org/10.1117/12.323792

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