Search results for " spline"
showing 10 items of 78 documents
2016
Gianluca Tramontana was supported by the GEOCARBON EU FP7 project (GA 283080). Dario Papale, Martin Jung and Markus Reichstein acknowledge funding from the EU FP7 project GEOCARBON (grant agreement no. 283080) and the EU H2020 BACI project (grant agreement no. 640176). Gustau Camps-Valls wants to acknowledge the support by an ERC Consolidator Grant with grant agreement 647423 (SEDAL). Kazuhito Ichii was supported by Environment Research and Technology Development Funds (2-1401) from the Ministry of the Environment of Japan and the JAXA Global Change Observation Mission (GCOM) project (no. 115). Christopher R. Schwalm was supported by National Aeronautics and Space Administration (NASA) gran…
Periodic Polynomial Splines
2018
In this chapter, the spaces of periodic polynomial splines and the Spline Harmonic Analysis (SHA) in these spaces are briefly outlined. The stuff of this chapter is used for the design of periodic discrete-time splines and discrete-time-spline-based wavelets and wavelet packets. For a detailed description of the subject we refer to (Averbuch, Neittaanmaki and Zheludev, Spline and Spline Wavelet Methods with Applications to Signal and Image Processing, Springer, Berlin, 2014) [1]. Periodic polynomial splines provide an example of mixed discrete-continuous circular convolution.
Cubic smoothing splines background correction in on-line liquid chromatography–Fourier transform infrared spectrometry
2010
A background correction method for the on-line coupling of gradient liquid chromatography and Fourier transform infrared spectrometry (LC-FTIR) is proposed. The developed approach applies univariate background correction to each variable (i.e. each wave number) individually. Spectra measured in the region before and after each peak cluster are used as knots to model the variation of the eluent absorption intensity with time using cubic smoothing splines (CSS) functions. The new approach has been successfully tested on simulated as well as on real data sets obtained from injections of standard mixtures of polyethylene glycols with four different molecular weights in methanol:water, 2-propano…
On spline methods of approximation under L-fuzzy information
2011
This work is closely related to our previous papers on algorithms of approximation under L-fuzzy information. In the classical theory of approximation central algorithms were worked out on the basis of usual, that is crisp splines. We describe central methods for solution of linear problems with balanced L-fuzzy information and develop the concept of L-fuzzy splines.
A filtering algorithm for maneuvering target tracking based on smoothing spline fitting
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/127643 Open Access Maneuvering target tracking is a challenge. Target's sudden speed or direction changing would make the common filtering tracker divergence. To improve the accuracy of maneuvering target tracking, we propose a tracking algorithm based on spline fitting. Curve fitting, based on historical point trace, reflects the mobility information. The innovation of this paper is assuming that there is no dynamic motion model, and prediction is only based on the curve fitting over the measured data. Monte Carlo simulation results show that, …
Non-periodic Polynomial Splines
2015
In this chapter, we outline the essentials of the splines theory. By themselves, they are of interest for signal processing research. We use the Zak transform to derive an integral representation of polynomial splines on uniform grids. The integral representation facilitated design of different generators of spline spaces and their duals. It provides explicit expressions for interpolating and smoothing splines of any order. In forthcoming chapters, the integral representation of splines will be used for the constructions of efficient subdivision schemes and so also for the design spline-based wavelets and wavelet frames.
Special Splines of Exponential Type for the Solutions of Mass Transfer Problems in Multilayer Domains
2016
We consider averaging methods for solving the 3-D boundary-value problem of second order in multilayer domain. The special hyperbolic and exponential type splines, with middle integral values of piece-wise smooth function interpolation are considered. With the help of these splines the problems of mathematical physics in 3-D with piece-wise coefficients are reduced with respect to one coordinate to 2-D problems. This procedure also allows to reduce the 2-D problems to 1-D problems and the solution of the approximated problemsa can be obtained analytically. In the case of constant piece-wise coefficients we obtain the exact discrete approximation of a steady-state 1-D boundary-value problem.…
Calculation of Splines Values by Subdivision
2014
Assume, the samples of a spline \(S(t)\in {}^{p}\fancyscript{S}\) on the grid \(\mathbf{g} =\{k\}_{k\in \mathbb {Z}}\) are available: \(S(k)=y[k]\). Subdivision schemes are proposed to calculate the spline’s values at dyadic and triadic rational points \(S(k/2^m)\) and \(S(k/3^m)\). The SHA technique provides fast and explicit implementation of the subdivision for one- and two-dimensional periodic splines.
Cell-Average Multiwavelets Based on Hermite Interpolation
2007
Polynomial Smoothing Splines
2014
Interpolating splines is a perfect tool for approximation of a continuous-time signal \(f(t)\) in the case when samples \(x[k]=f(k),\;k\in \mathbb {Z}\) are available. However, frequently, the samples are corrupted by random noise. In such case, the so-called smoothing splines provide better approximation. In this chapter we describe periodic smoothing splines in one and two dimensions. The SHA technique provides explicit expression of such splines and enables us to derive optimal values of the regularization parameters.