Signal Reconstruction From Multiple Unregistered Sets Of Samples Using Groebner Bases

Author

Vandewalle, Patrick ; Sbaiz, Luciano ; Vetterli, Martin

Author_Institution

LCAV, Ecole Polytech. Fed. de Lausanne

Volume

3

fYear

2006

fDate

14-19 May 2006

Abstract

We present a new method for signal reconstruction from multiple sets of samples with unknown offsets. We rewrite the reconstruction problem as a set of polynomial equations in the unknown signal parameters and the offsets between the sets of samples. Then, we construct a Grobner basis for the corresponding affine variety. The signal parameters can then easily be derived from this Grobner basis. This provides us with an elegant solution method for the initial nonlinear problem. We show two examples for the reconstruction of polynomial signals and Fourier series

Keywords

Fourier series; matrix algebra; polynomials; signal reconstruction; Fourier series; Groebner bases; nonlinear problem; polynomial equations; polynomial signals; signal reconstruction; Fourier series; Geometry; High-resolution imaging; Image reconstruction; Image resolution; Nonlinear equations; Polynomials; Reconstruction algorithms; Signal reconstruction; Signal resolution;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech and Signal Processing, 2006. ICASSP 2006 Proceedings. 2006 IEEE International Conference on

Conference_Location

Toulouse

ISSN

1520-6149

Print_ISBN

1-4244-0469-X

Type

conf

DOI

10.1109/ICASSP.2006.1660726

Filename

1660726