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A new method of solving noisy Abel-type equations

Garza, J; Hall, Peter; Ruymgaart, F


A new approach to solving noisy integral equations of the first kind is applied to the family of Abel equations. Such equations play a role in stereology (Wicksell's unfolding problem), medicine, engineering, and astronomy. The method is based on an expansion in an arbitrary orthonormal basis, coupled with exact inversion of the integral operator. The inverse appears in the Fourier coefficients of the expansion, where it can be carried over to the usually well-behaved basis elements in the form...[Show more]

CollectionsANU Research Publications
Date published: 2001
Type: Journal article
Source: Journal of Mathematical Analysis and Applications
DOI: 10.1006/jmaa.2000.7371


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