Publication

Signal Reconstruction from Multiple Unregistered Sets of Samples using Groebner Bases

Martin Vetterli, Luciano Sbaiz, Patrick Vandewalle
2006
Conference Papers

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 Groebner basis for the corresponding affine variety. The signal parameters can then easily be derived from this Groebner 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.

Official source

https://infoscience.epfl.ch/entities/publication/47a0fe09-5efe-4c95-aac4-39bb823d9bf0

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Martin Vetterli, Luciano Sbaiz, Patrick Vandewalle
2006
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/47a0fe09-5efe-4c95-aac4-39bb823d9bf0

About this result

Related concepts (32)

System of polynomial equations

A system of polynomial equations (sometimes simply a polynomial system) is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k. A solution of a polynomial system is a set of values for the xis which belong to some algebraically closed field extension K of k, and make all equations true. When k is the field of rational numbers, K is generally assumed to be the field of complex numbers, because each solution belongs to a field extension of k, which is isomorphic to a subfield of the complex numbers.

Set (mathematics)

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics.

Gröbner basis

In mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring K[x1, ..., xn] over a field K. A Gröbner basis allows many important properties of the ideal and the associated algebraic variety to be deduced easily, such as the dimension and the number of zeros when it is finite.

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