Zobrazeno 1 - 10
of 29
pro vyhledávání: '"44A12, 65R32"'
Autor:
Aramyan, Rafik
Hyperplane is a set of non-injectivity of the spherical Radon transform (SRT) in the space of continuous functions in R^d. In this article, for the reconstruction of an unknown function f from C(R^3) (the support can be non-compact), using the spheri
Externí odkaz:
http://arxiv.org/abs/2404.04630
For an integer $r\ge0$, we prove the $r$th order Reshetnyak formula for the ray transform of rank $m$ symmetric tensor fields on $\mathbb{R}^n$. Certain differential operators $A^{(m,r,l)}\ (0\le l\le r)$ on the sphere $\mathbb{S}^{n-1}$ are main ing
Externí odkaz:
http://arxiv.org/abs/2106.11624
We propose a novel direct sampling method (DSM) for the effective and stable inversion of the Radon transform. The DSM is based on a generalization of the important almost orthogonality property in classical DSMs to fractional order Sobolev duality p
Externí odkaz:
http://arxiv.org/abs/2010.10945
Tomographic image reconstruction is well understood if the specimen being studied is stationary during data acquisition. However, if this specimen changes during the measuring process, standard reconstruction techniques can lead to severe motion arte
Externí odkaz:
http://arxiv.org/abs/2009.04212
Publikováno v:
Journal of Inverse and Ill-posed Problems, vol. 31, no. 1, 2023, pp. 43-63
The geodesic ray transform, the mixed ray transform and the transverse ray transform of a tensor field on a manifold can all be seen as what we call mixing ray transforms, compositions of the geodesic ray transform and an invertible linear map on ten
Externí odkaz:
http://arxiv.org/abs/2009.01043
The momentum ray transform $I^k$ integrates a rank $m$ symmetric tensor field $f$ over lines of ${\R}^n$ with the weight $t^k$: $ (I^k\!f)(x,\xi)=\int_{-\infty}^\infty t^k\l f(x+t\xi),\xi^m\r\,dt. $ We give the range characterization for the operator
Externí odkaz:
http://arxiv.org/abs/1909.07682
Autor:
Ilmavirta, Joonas, Railo, Jesse
Publikováno v:
Ann. Acad. Sci. Fenn. Math. 45 (2020), 1095--1102
We show injectivity of the geodesic X-ray transform on piecewise constant functions when the transform is weighted by a continuous matrix weight. The manifold is assumed to be compact and nontrapping of any dimension, and in dimension three and highe
Externí odkaz:
http://arxiv.org/abs/1901.03525
The momentum ray transform $I^k$ integrates a rank $m$ symmetric tensor field $f$ over lines with the weight $t^k$: $ (I^k\!f)(x,\xi)=\int_{-\infty}^\infty t^k\langle f(x+t\xi),\xi^m\rangle\,dt. $ In particular, the ray transform $I=I^0$ was studied
Externí odkaz:
http://arxiv.org/abs/1808.00768
Autor:
Zhang, Yang
We study the integral transform over a general family of broken rays in $\mathbb{R}^2$. It is natural for broken rays to have conjugate points, for example, when they are reflected from a curved boundary. If there are conjugate points, we show that t
Externí odkaz:
http://arxiv.org/abs/1711.08575
Autor:
Andén, Joakim, Singer, Amit
In cryo-electron microscopy, the 3D electric potentials of an ensemble of molecules are projected along arbitrary viewing directions to yield noisy 2D images. The volume maps representing these potentials typically exhibit a great deal of structural
Externí odkaz:
http://arxiv.org/abs/1710.09791