Title :
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
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;
Conference_Titel :
Acoustics, Speech and Signal Processing, 2006. ICASSP 2006 Proceedings. 2006 IEEE International Conference on
Conference_Location :
Toulouse
Print_ISBN :
1-4244-0469-X
DOI :
10.1109/ICASSP.2006.1660726
