L1C1 polynomial spline approximation algorithms for large data sets

Olivier Gibaru 1, 2 Laurent Gajny 2 Eric Nyiri 2
1 NON-A - Non-Asymptotic estimation for online systems
CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189, Inria Lille - Nord Europe
Abstract : In this article, we address the problem of approximating data points by C1-smooth polynomial spline curves or surfaces using L1-norm. The use of this norm helps to preserve the data shape and it reduces extraneous oscillations. In our approach, we introduce a new functional which enables to control directly the distance between the data points and the resulting spline solution. The omputational complexity of the minimization algorithm is nonlinear. A local minimization method using sliding windows allows to compute approximation splines within a linear complexity. This strategy seems to be more robust than a global method when applied on large data sets. When the data are noisy, we iteratively apply this method to globally smooth the solution while preserving the data shape. This method is applied to image denoising.
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https://hal.inria.fr/hal-00927555
Contributor : Olivier Gibaru <>
Submitted on : Monday, January 13, 2014 - 11:49:34 AM
Last modification on : Tuesday, April 2, 2019 - 2:03:22 AM

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Olivier Gibaru, Laurent Gajny, Eric Nyiri. L1C1 polynomial spline approximation algorithms for large data sets. Numerical Algorithms, Springer Verlag, 2013, ⟨10.1007/s11075-014-9828-x⟩. ⟨hal-00927555⟩

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