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Using wavelet methods to solve noisy Abel-type equations with discontinuous inputs

Hall, Peter; Paige, Robert; Ruymgaart, Frits

Description

One way of estimating a function from indirect, noisy measurements is to regularise an inverse of its Fourier transformation, using properties of the adjoint of the transform that degraded the function in the first place. It is known that when the function is smooth, this approach can perform well and produce estimators that have optimal convergence rates. When the function is unsmooth, in particular when it suffers jump discontinuities, an analogue of this approach is to invert the wavelet...[Show more]

CollectionsANU Research Publications
Date published: 2003
Type: Journal article
URI: http://hdl.handle.net/1885/76445
Source: Journal of Multivariate Analysis
DOI: 10.1016/S0047-259X(02)00043-X

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