A discrete Funk transform on the Cubed Sphere

نویسندگان

چکیده

Computing accurately Funk transforms from discrete values is crucial in some applications, such as Q-Ball Imaging medicine. This paper deals with a transform devoted to computation. The studied based on spectral method applied least squares fitting, the special feature that regularization not performed. We investigate several mathematical and numerical aspects this context, including stability pseudoinversion. As specific instance, we introduce simple framework equiangular Cubed Sphere guarantee stability. Various experiments attest accuracy convergence of approach, particular for synthetic Gaussian signals Imaging.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Schwarz Preconditioner for the Cubed-Sphere

A spectral element formulation of the atmospheric two-dimensional shallow water equations on the cubed-sphere is described. The equations are written in tensor form using the contravariant and covariant velocity components. A semi-implicit time discretization results in a reduced Schur complement system for the pressure. The Laplacian operator is approximated by the L2 pseudo-Laplacian arising ...

متن کامل

A Discontinuous Galerkin Transport Scheme on the Cubed Sphere

A conservative transport scheme based on the discontinuous Galerkin (DG) method has been developed for the cubed sphere. Two different central projection methods, equidistant and equiangular, are employed for mapping between the inscribed cube and the sphere. These mappings divide the spherical surface into six identical subdomains, and the resulting grid is free from singularities. Two standar...

متن کامل

Generalized Minkowski-funk Transforms and Small Denominators on the Sphere

The Cauchy problem for the Euler-Poisson-Darboux equation on the unit sphere Sn gives rise to a family of fractional integrals M cos f(x) which integrate f over the spherical cap of radius centered at the point x 2 Sn. These fractional integrals are called the generalized Minkowski-Funk transforms because various transforms of integral geometry (including those of Minkowski and Funk) are partic...

متن کامل

Sampling Theorem and Discrete Fourier Transform on the Riemann Sphere ∗

Using coherent-state techniques, we prove a sampling theorem for Majorana's (holomor-phic) functions on the Riemann sphere and we provide an exact reconstruction formula as a convolution product of N samples and a given reconstruction kernel (a sinc-type function). We also discuss the effect of over-and under-sampling. Sample points are roots of unity, a fact which allows explicit inversion for...

متن کامل

Hermitian Compact Interpolation on the Cubed-Sphere Grid

The cubed-sphere grid is a spherical grid made of six quasi-cartesian square-like patches. It was originally introduced in [21]. We extend to this grid the design of high-order nite-di erence compact operators [4, 11]. The present work is limitated to the design of a fourth-order accurate spherical gradient. The treatment at the interface of the six patches relies on a speci c interpolation sys...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

ژورنال

عنوان ژورنال: Journal of Computational and Applied Mathematics

سال: 2023

ISSN: ['0377-0427', '1879-1778', '0771-050X']

DOI: https://doi.org/10.1016/j.cam.2023.115205