Exact recovery of non-uniform splines from the projection onto spaces of\n algebraic polynomials

2014/12/19 by Tamir Bendory, Shai Dekel, Bendory, Tamir +3
Computer Science · Engineering · Mathematics · #Advanced Computational Techniques in Science and Engineering #Advanced Numerical Analysis Techniques #FOS: Computer and information sciences #FOS: Mathematics #Image and Signal Denoising Methods #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1412.6254

openalex publication_date 2014/12/19 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

In this work we consider the problem of recovering non-uniform splines from\ntheir projection onto spaces of algebraic polynomials. We show that under a\ncertain Chebyshev-type separation condition on its knots, a spline whose\ninner-products with a polynomial basis and boundary conditions are known, can\nbe recovered using Total Variation norm minimization. The proof of the\nuniqueness of the solution uses the method of `dual' interpolating polynomials\nand is based on citeSR, where the theory was developed for trigonometric\npolynomials. We also show results for the multivariate case.\n

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