Search results for "INTERPOLATION"
showing 10 items of 331 documents
Data analysis procedures for pulse ELDOR measurements of broad distance distributions
2004
The reliability of procedures for extracting the distance distribution between spins from the dipolar evolution function is studied with particular emphasis on broad distributions. A new numerically stable procedure for fitting distance distributions with polynomial interpolation between sampling points is introduced and compared to Tikhonov regularization in the dipolar frequency and distance domains and to approximate Pake transformation. Distance distributions with only narrow peaks are most reliably extracted by distance-domain Tikhonov regularization, while frequency-domain Tikhonov regularization is favorable for distributions with only broad peaks. For the quantification of distribut…
Rational Hermite Interpolation and Quadrature
1993
Rational Hermite interpolation is used in two different ways in order to derive and analyze quadrature rules. One approach yields quadratures of Gaussian-type whereas the other one generalizes Engels’ dual quadratures exhibiting the close connection between rational Hermite interpolation and quadrature in general.
A neural network clustering algorithm for the ATLAS silicon pixel detector
2014
A novel technique to identify and split clusters created by multiple charged particles in the ATLAS pixel detector using a set of artificial neural networks is presented. Such merged clusters are a common feature of tracks originating from highly energetic objects, such as jets. Neural networks are trained using Monte Carlo samples produced with a detailed detector simulation. This technique replaces the former clustering approach based on a connected component analysis and charge interpolation. The performance of the neural network splitting technique is quantified using data from proton-proton collisions at the LHC collected by the ATLAS detector in 2011 and from Monte Carlo simulations. …
Resolution enhancement in integral microscopy by physical interpolation
2015
Integral-imaging technology has demonstrated its capability for computing depth images from the microimages recorded after a single shot. This capability has been shown in macroscopic imaging and also in microscopy. Despite the possibility of refocusing different planes from one snap-shot is crucial for the study of some biological processes, the main drawback in integral imaging is the substantial reduction of the spatial resolution. In this contribution we report a technique, which permits to increase the two-dimensional spatial resolution of the computed depth images in integral microscopy by a factor of √2. This is made by a double-shot approach, carried out by means of a rotating glass…
Higher Order Sobolev-Type Spaces on the Real Line
2014
This paper gives a characterization of Sobolev functions on the real line by means of pointwise inequalities involving finite differences. This is also shown to apply to more general Orlicz-Sobolev, Lorentz-Sobolev, and Lorentz-Karamata-Sobolev spaces.
On Inverse Distance Weighting in Pollution Models
2011
When evaluating the impact of pollution, measurements from remote stations are often weighted by the inverse of distance raised to some nonnegative power (IDW). This is derived from Shepard's method of spatial interpolation (1968). The paper discusses the arbitrary character of the exponent of distance and the problem of monitoring stations that are close to the reference point. From elementary laws of physics, it is determined which exponent of distance should be chosen (or its upper bound) depending on the form of pollution encountered, such as radiant pollution (including radioactivity and sound), air pollution (plumes, puffs, and motionless clouds by using the classical Gaussian model),…
Pollution models and inverse distance weighting: some critical remarks
2013
International audience; When evaluating the impact of pollution, measurements from remote stations are often weighted by the inverse of distance raised to some nonnegative power (IDW). This is derived from Shepard's method of spatial interpolation (1968). The paper discusses the arbitrary character of the exponent of distance and the problem of monitoring stations that are close to the reference point. From elementary laws of physics, it is determined which exponent of distance should be chosen (or its upper bound) depending on the form of pollution encountered, such as radiant pollution (including radioactivity and sound), air pollution (plumes, puffs, and motionless clouds by using the cl…
Study and construction of the quasi-linear subdivision schemes over bi-regular meshs
2012
Subdivision schemes are commonly used to generate a smooth shape from a much more coarseone. The reverse subdivision is designed to describe a high resolution mesh from a coarse one. Bothof these tools are used in numerous graphical modelisation domains. In this thesis, we focused ontwo distinct aspects: on one hand the construction of quasi-linear subdivision schemes and on theother hand the construction of reverse quad/triangle subdivision schemes. The work, presented inthe context of the subdivision, describes the construction of a new type of subdivision schemes, andtheirs applications to solve some problems coming from the application of linear subdivision schemes.The work presented in…
On specific stability bounds for linear multiresolution schemes based on piecewise polynomial Lagrange interpolation
2009
Abstract The Deslauriers–Dubuc symmetric interpolation process can be considered as an interpolatory prediction scheme within Harten's framework. In this paper we express the Deslauriers–Dubuc prediction operator as a combination of either second order or first order differences. Through a detailed analysis of certain contractivity properties, we arrive to specific l ∞ -stability bounds for the multiresolution transform. A variety of tests indicate that these l ∞ bounds are closer to numerical estimates than those obtained with other approaches.
Wavelet Frames Generated by Perfect Reconstruction Filter Banks
2015
It was indicated in Sect. 2.2 that oversampled perfect reconstruction (PR) filter banks generate specific types of frames in the signal space. In this chapter, a family of tight and semi-tight frames is presented. The three- and four-channel filter banks that generate the framed originate from polynomial and discrete splines. Those frames have properties, which are attractive for signal processing, such as symmetry, interpolation, flat spectra. These properties are combined with fine time-domain localization and efficient implementation. This family includes framelets, that have any number of discrete vanishing moments. Non-compactness of their supports is compensated by exponential decay o…