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Rapport Année : 2014

Non-uniform spline recovery from small degree polynomial approximation

Résumé

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. Finally, we study the localization of the knots of non-uniform splines from small degree polynomial approximations.
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Dates et versions

hal-00950850 , version 1 (23-02-2014)
hal-00950850 , version 2 (25-05-2015)

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Yohann de Castro, Guillaume Mijoule. Non-uniform spline recovery from small degree polynomial approximation. 2014. ⟨hal-00950850v1⟩
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