Search results for "interpolation."
showing 10 items of 253 documents
Impulsive control of the bilinear Schrödinger equation: propagators and attainable sets
2019
International audience; We consider a linear Schrödinger equation with an unbounded bilinear control term. The control term is the derivative of function with bounded variations (impulsive control). Well-posedness results and regularity of the associated propagators follow from classical theory from Kato. As a byproduct, one obtains a topological obstruction to exact controllability of the system in the spirit of the results of Ball, Marsden and Slemrod.
A Generalised RBF Finite Difference Approach to Solve Nonlinear Heat Conduction Problems on Unstructured Datasets
2011
Radial Basis Functions have traditionally been used to provide a continuous interpolation of scattered data sets. However, this interpolation also allows for the reconstruction of partial derivatives throughout the solution field, which can then be used to drive the solution of a partial differential equation. Since the interpolation takes place on a scattered dataset with no local connectivity, the solution is essentially meshless. RBF-based methods have been successfully used to solve a wide variety of PDEs in this fashion. Such full-domain RBF methods are highly flexible and can exhibit spectral convergence rates Madych & Nelson (1990). However, in their traditional implementation the fu…
Remarks on the semivariation of vector measures with respect to Banach spaces.
2007
Suppose that and . It is shown that any Lp(µ)-valued measure has finite L2(v)-semivariation with respect to the tensor norm for 1 ≤ p < ∞ and finite Lq(v)-semivariation with respect to the tensor norm whenever either q = 2 and 1 ≤ p ≤ 2 or q > max{p, 2}. However there exist measures with infinite Lq-semivariation with respect to the tensor norm for any 1 ≤ q < 2. It is also shown that the measure m (A) = χA has infinite Lq-semivariation with respect to the tensor norm if q < p.
Commutators of linear and bilinear Hilbert transforms
2003
Let α ∈ R \alpha \in \mathbb {R} , and let H α ( f , g ) ( x ) = 1 π p . v . ∫ f ( x − t ) g ( x − α t ) d t t H_\alpha (f,g)(x)=\frac {1}{\pi } p.v. \int f(x-t)g(x-\alpha t)\frac {dt}{t} and H f ( x ) = 1 π p . v . ∫ f ( x − t ) d t t Hf(x)= \frac {1}{\pi } p.v.\int f(x-t)\frac {dt}{t} denote the bilinear and linear Hilbert transforms, respectively. It is proved that, for 1 > p > ∞ 1>p>\infty and α 1 ≠ α 2 \alpha _1\ne \alpha _2 , H α 1 − H α 2 H_{\alpha _1}-H_{\alpha _2} maps L p × B M O L^p\times BMO into L p L^{p} and it maps B M O × L p BMO \times L^p into L p L^{p} if and only if sign ( α 1 ) = sign ( α 2 ) \operatorname {sign}(\alpha _1)=\operatorname {sign}(\alpha _2…
Extension of luminance component based demosaicking algorithm to 4- and 5-band multispectral images
2021
Abstract Multispectral imaging systems are currently expanding with a variety of multispectral demosaicking algorithms. But these algorithms have limitations due to the remarkable presence of artifacts in the reconstructed image. In this paper, we propose a powerful multispectral image demosaicking method that focuses on the G band and luminance component. We've first identified a relevant 4-and 5-band multispectral filter array (MSFA) with the dominant G band and then proposed an algorithm that consistently estimates the missing G values and other missing components using a convolution operator and a weighted bilinear interpolation algorithm based on the luminance component. Using the cons…
An abstract inf-sup problem inspired by limit analysis in perfect plasticity and related applications
2021
This paper is concerned with an abstract inf-sup problem generated by a bilinear Lagrangian and convex constraints. We study the conditions that guarantee no gap between the inf-sup and related sup-inf problems. The key assumption introduced in the paper generalizes the well-known Babuška–Brezzi condition. It is based on an inf-sup condition defined for convex cones in function spaces. We also apply a regularization method convenient for solving the inf-sup problem and derive a computable majorant of the critical (inf-sup) value, which can be used in a posteriori error analysis of numerical results. Results obtained for the abstract problem are applied to continuum mechanics. In particular…
Fake Nodes approximation for Magnetic Particle Imaging
2020
Accurately reconstructing functions with discontinuities is the key tool in many bio-imaging applications as, for instance, in Magnetic Particle Imaging (MPI). In this paper, we apply a method for scattered data interpolation, named mapped bases or Fake Nodes approach, which incorporates discontinuities via a suitable mapping function. This technique naturally mitigates the Gibbs phenomenon, as numerical evidence for reconstructing MPI images confirms.
Optimal Filter Estimation for Lucas-Kanade Optical Flow
2012
Optical flow algorithms offer a way to estimate motion from a sequence of images. The computation of optical flow plays a key-role in several computer vision applications, including motion detection and segmentation, frame interpolation, three-dimensional scene reconstruction, robot navigation and video compression. In the case of gradient based optical flow implementation, the pre-filtering step plays a vital role, not only for accurate computation of optical flow, but also for the improvement of performance. Generally, in optical flow computation, filtering is used at the initial level on original input images and afterwards, the images are resized. In this paper, we propose an image filt…
Three-dimensional Fuzzy Kernel Regression framework for registration of medical volume data
2013
Abstract In this work a general framework for non-rigid 3D medical image registration is presented. It relies on two pattern recognition techniques: kernel regression and fuzzy c-means clustering. The paper provides theoretic explanation, details the framework, and illustrates its application to implement three registration algorithms for CT/MR volumes as well as single 2D slices. The first two algorithms are landmark-based approaches, while the third one is an area-based technique. The last approach is based on iterative hierarchical volume subdivision, and maximization of mutual information. Moreover, a high performance Nvidia CUDA based implementation of the algorithm is presented. The f…
A Parallel Approach to HRTF Approximation and Interpolation Based on a Parametric Filter Model
2017
[EN] Spatial audio-rendering techniques using head-related transfer functions (HRTFs) are currently used in many different contexts such as immersive teleconferencing systems, gaming, or 3-D audio reproduction. Since all these applications usually involve real-time constraints, efficient processing structures for HRTF modeling and interpolation are necessary for providing real-time binaural audio solutions. This letter presents a parametric parallel model that allows us to perform HRTF filtering and interpolation efficiently from an input HRTF dataset. The resulting model, which is an adaptation from a recently proposed modeling technique, not only reduces the size of HRTF datasets signific…