Search results for "Smoothing spline"
showing 5 items of 15 documents
Quasi-interpolating and Smoothing Local Splines
2015
In this chapter, local quasi-interpolating and smoothing splines are described. Although approximation properties of local spline are similar to properties of the global interpolating and smoothing splines, their design does not require the IIR filtering of the whole data array. The computation of a local spline value at some point utilizes only a few adjacent grid samples. Therefore, local splines can be used for real-time processing of signals and for the design of FIR filter banks generating wavelets and wavelet frames (Chaps. 12 and 14). In the chapter, local splines of different orders are designed and their approximation properties are established which are compared with the propertie…
Spline Algorithms for Deconvolution and Inversion of Heat Equation
2014
In this chapter, we present algorithms based on Tikhonov regularization for solving two related problems: deconvolution and inversion of heat equation. The algorithms, which utilize the SHA technique, provide explicit solutions to the problems in one and two dimensions.
Fast Computation by Subdivision of Multidimensional Splines and Their Applications
2016
We present theory and algorithms for fast explicit computations of uni- and multi-dimensional periodic splines of arbitrary order at triadic rational points and of splines of even order at diadic rational points. The algorithms use the forward and the inverse Fast Fourier transform (FFT). The implementation is as fast as FFT computation. The algorithms are based on binary and ternary subdivision of splines. Interpolating and smoothing splines are used for a sample rate convertor such as resolution upsampling of discrete-time signals and digital images and restoration of decimated images that were contaminated by noise. The performance of the rate conversion based spline is compared with the…
ON SOME GENERALIZATION OF SMOOTHING PROBLEMS
2015
The paper deals with the generalized smoothing problem in abstract Hilbert spaces. This generalized problem involves particular cases such as the interpolating problem, the smoothing problem with weights, the smoothing problem with obstacles, the problem on splines in convex sets and others. The theorem on the existence and characterization of a solution of the generalized problem is proved. It is shown how the theorem gives already known theorems in special cases as well as some new results.
Noise Reduction and Gap Filling of fAPAR Time Series Using an Adapted Local Regression Filter
2014
Time series of remotely sensed data are an important source of information for understanding land cover dynamics. In particular, the fraction of absorbed photosynthetic active radiation (fAPAR) is a key variable in the assessment of vegetation primary production over time. However, the fAPAR series derived from polar orbit satellites are not continuous and consistent in space and time. Filtering methods are thus required to fill in gaps and produce high-quality time series. This study proposes an adapted (iteratively reweighted) local regression filter (LOESS) and performs a benchmarking intercomparison with four popular and generally applicable smoothing methods: Double Logistic (DLOG), sm…