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Exact recovery of non-uniform splines from the projection onto spaces of algebraic polynomials (1412.6254v1)
Published 19 Dec 2014 in cs.IT, math.IT, and math.NA
Abstract: In this work we consider the problem of recovering non-uniform splines from their projection onto spaces of algebraic polynomials. We show that under a certain Chebyshev-type separation condition on its knots, a spline whose inner-products with a polynomial basis and boundary conditions are known, can be recovered using Total Variation norm minimization. The proof of the uniqueness of the solution uses the method of `dual' interpolating polynomials and is based on \cite{SR}, where the theory was developed for trigonometric polynomials. We also show results for the multivariate case.