The Generalized Annihilation Property:A Tool For Solving Finite Rate of Innovation ProblemsReportar como inadecuado




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1 Department of Electronic Engineering Hong Kong

Abstract : We describe a property satisfied by a class of nonlinear systems of equations that are of the form FOmegaX = Y. Here FOmega is a matrix that depends on an unknown K-dimensional vector Omega, X is an unknown K-dimensional vector and Y is a vector of N >= K given measurements. Such equations are encountered in superresolution or sparse signal recovery problems known as -Finite Rate of Innovation- signal reconstruction. We show how this property allows to solve explicitly for the unknowns Omega and X by a direct, non-iterative, algorithm that involves the resolution of two linear systems of equations and the extraction of the roots of a polynomial and give examples of problems where this type of solutions has been found useful.





Autor: Thierry Blu -

Fuente: https://hal.archives-ouvertes.fr/



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