Non-uniform spline recovery from small degree polynomial approximation

Yohann De Castro; Guillaume Mijoule

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arXiv · 1402.5662

Non-uniform spline recovery from small degree polynomial approximation

Yohann De Castro·Guillaume Mijoule

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Abstract

We investigate the sparse spikes deconvolution problem onto spaces of algebraic polynomials. Our framework encompasses the measure reconstruction problem from a combination of noiseless and noisy moment measurements. We study a TV-norm regularization procedure to localize the support and estimate the weights of a target discrete measure in this frame. Furthermore, we derive quantitative bounds on the support recovery and the amplitudes errors under a Chebyshev-type minimal separation condition on its support. Incidentally, we study the localization of the knots of non-uniform splines when a Gaussian perturbation of their inner-products with a known polynomial basis is observed (i.e. a small degree polynomial approximation is known) and the boundary conditions are known. We prove that the knots can be recovered in a grid-free manner using semidefinite programming.

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Yohann De Castro, Guillaume Mijoule. 2014-02-23. Non-uniform spline recovery from small degree polynomial approximation. https://arxiv.org/abs/1402.5662

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