Journal ArticleDOI
On azimuthally symmetric 2-sphere convolution
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TLDR
A simpler framework to understand, use and generalize azimuthally symmetric convolution of signals defined on the 2-Sphere is demonstrated.About:
This article is published in Digital Signal Processing.The article was published on 2011-09-01. It has received 32 citations till now. The article focuses on the topics: Symmetric convolution & Convolution power.read more
Citations
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Hilbert Space Methods in Signal Processing
TL;DR: In this article, the authors introduce the concept of Hilbert spaces and introduce operators, including bounded operators, compact operators, and integral operators, for signal concentration and joint spatio-spectral analysis on 2-sphere.
Journal ArticleDOI
Towards unconstrained compartment modeling in white matter using diffusion-relaxation MRI with tensor-valued diffusion encoding.
Björn Lampinen,Filip Szczepankiewicz,Filip Szczepankiewicz,Johan Mårtensson,Danielle van Westen,Oskar Hansson,Carl-Fredrik Westin,Markus Nilsson +7 more
TL;DR: To optimize diffusion‐relaxation MRI with tensor‐valued diffusion encoding for precise estimation of compartment‐specific fractions, diffusivities, and T2 values within a two‐compartment model of white matter, and to explore the approach in vivo.
Journal ArticleDOI
An Optimal-Dimensionality Sampling Scheme on the Sphere With Fast Spherical Harmonic Transforms
TL;DR: A sampling scheme on the sphere that permits accurate computation of the spherical harmonic transform and its inverse for signals band-limited at L using only L2 samples and obtains the optimal number of samples given by the degrees of freedom of the signal in harmonic space.
Journal ArticleDOI
Measuring compartmental T2-orientational dependence in human brain white matter using a tiltable RF coil and diffusion-T2 correlation MRI.
Chantal M. W. Tax,Chantal M. W. Tax,Elena Kleban,Maxime Chamberland,Muhamed Barakovic,Umesh S. Rudrapatna,Derek K. Jones +6 more
TL;DR: These observations have the potential to lead to white matter microstructural models with increased compartmental sensitivity to disease, and can have direct consequences for longitudinal and group-wise T2- and diffusion-MRI data analysis, where the effect of head-orientation in the scanner is commonly ignored.
Journal ArticleDOI
Fast Directional Spatially Localized Spherical Harmonic Transform
TL;DR: Since such typical data-sets on the sphere are of considerable size and the directional SLSHT is intrinsically computationally demanding depending on the band-limits of the signal and window, a fast algorithm for the efficient computation of the transform is developed.
References
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Journal ArticleDOI
HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere
Krzysztof M. Gorski,Krzysztof M. Gorski,E. Hivon,A. J. Banday,Benjamin D. Wandelt,F. K. Hansen,Mstvos Reinecke,Matthia Bartelmann +7 more
TL;DR: This paper considers the requirements and implementation constraints on a framework that simultaneously enables an efficient discretization with associated hierarchical indexation and fast analysis/synthesis of functions defined on the sphere and demonstrates how these are explicitly satisfied by HEALPix.
Book
Inverse Acoustic and Electromagnetic Scattering Theory
David Colton,Rainer Kress +1 more
TL;DR: Inverse Medium Problem (IMP) as discussed by the authors is a generalization of the Helmholtz Equation for direct acoustical obstacle scattering in an Inhomogeneous Medium (IMM).
Journal ArticleDOI
HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
Krzysztof M. Gorski,E. Hivon,A. J. Banday,Benjamin D. Wandelt,F. K. Hansen,Martin Reinecke,M. Bartelman +6 more
TL;DR: The Hierarchical Equal Area iso-Latitude Pixelization (HEALPix) as discussed by the authors is a data structure with an associated library of computational algorithms and visualization software that supports fast scientific applications executable directly on very large volumes of astronomical data and large area surveys in the form of discretized spherical maps.
Journal ArticleDOI
Computing Fourier Transforms and Convolutions on the 2-Sphere
James R. Driscoll,D. M. Healy +1 more
TL;DR: Convolution theorems generalizing well known and useful results from the abelian case are used to develop a sampling theorem on the sphere, which reduces the calculation of Fourier transforms and convolutions of band-limited functions to discrete computations.
Book
Introduction to Hilbert spaces with applications
TL;DR: An overview of the basic ideas and results of Hilbert space theory and functional analysis can be found in the introduction to Hilbert spaces, Second Edition as mentioned in this paper, which acquaints students with the Lebesque integral and includes an enhanced presentation of results and proofs.