The reconstruction of a band-limited function and its Fourier transform from a finite number of samples at arbitrary locations by singular value decomposition

Author

Wingham, Duncan J.

Author_Institution

Dept. of Electron. & Electr. Eng., Univ. Coll., London, UK

Volume

40

Issue

3

fYear

1992

fDate

3/1/1992 12:00:00 AM

Firstpage

559

Lastpage

570

Abstract

A method for the stable interpolation of a bandlimited function known at sample instants with arbitrary locations in the presence of noise is given. Singular value decomposition is used to provide a series expansion that, in contrast to the method of sampling functions, permits simple identification of vectors in the minimum-norm space poorly represented in the sample values. Three methods, Miller regularization, least squares estimation, and maximum a posteriori estimation, are given for obtaining regularized reconstructions when noise is present. The singular value decomposition (SVD) method is used to interrelate these methods. Examples illustrating the technique are given

Keywords

Fourier transforms; interpolation; signal synthesis; Fourier transform; SVD; band-limited function; bandlimited function; interpolation; least squares estimation; maximum a posteriori estimation; minimum-norm space; regularized reconstructions; sampling functions; series expansion; singular value decomposition; vectors identification; Extraterrestrial measurements; Fourier transforms; Geophysical measurements; Geophysics computing; Image reconstruction; Interpolation; Least squares approximation; Maximum a posteriori estimation; Sampling methods; Singular value decomposition;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.120799

Filename

120799