Zobrazeno 1 - 10
of 28
pro vyhledávání: '"Abhishek, Anuj"'
Autor:
Abhishek, Anuj, Strauss, Thilo
In this work, we consider the non-invasive medical imaging modality of Electrical Impedance Tomography, where the problem is to recover the conductivity in a medium from a set of data that arises out of a current-to-voltage map (Neumann-to-Dirichlet
Externí odkaz:
http://arxiv.org/abs/2407.17182
In this article, we propose a non-parametric Bayesian level-set method for simultaneous reconstruction of piecewise constant diffusion and absorption coefficients in diffuse optical tomography (DOT). We show that the Bayesian formulation of the corre
Externí odkaz:
http://arxiv.org/abs/2404.11552
Local reconstruction analysis of inverting the Radon transform in the plane from noisy discrete data
In this paper, we investigate the reconstruction error, $N_\e^{\text{rec}}(x)$, when a linear, filtered back-projection (FBP) algorithm is applied to noisy, discrete Radon transform data with sampling step size $\epsilon$ in two-dimensions. Specifica
Externí odkaz:
http://arxiv.org/abs/2403.12909
We propose to combine the Carleman estimate and the Newton method to solve an inverse source problem for nonlinear parabolic equations from lateral boundary data. The stability of this inverse source problem is conditionally logarithmic. Hence, numer
Externí odkaz:
http://arxiv.org/abs/2209.08011
Publikováno v:
In Journal of Computational and Applied Mathematics 1 August 2024 445
Autor:
Abhishek, Anuj, Arya, Sakshi
In this article we propose a locally adaptive strategy for estimating a function from its Exponential Radon Transform (ERT) data, without prior knowledge of the smoothness of functions that are to be estimated. We build a non-parametric kernel type e
Externí odkaz:
http://arxiv.org/abs/2011.06887
Autor:
Abhishek, Anuj
In this article, we consider the problem of inverting the exponential Radon transform of a function in the presence of noise. We propose a kernel estimator to estimate the true function, analogous to the one proposed by Korostel\"{e}v and Tsybakov in
Externí odkaz:
http://arxiv.org/abs/2009.07131
Autor:
Abhishek, Anuj
Let (M, g) be a simple, real analytic, Riemannian manifold with boundary and of dimension n>=3. In this work, we prove a support theorem for the transverse ray transform of tensor fields of rank 2 defined over such manifolds. More specifically, given
Externí odkaz:
http://arxiv.org/abs/1804.03796
Autor:
Abhishek, Anuj, Mishra, Rohit Kumar
In this work, we show an injectivity result and support theorems for integral moments of a m-tensor field on a simple, real analytic, Riemannian manifold. Integral moments of m-tensor field were first introduced by Sharafutdinov. At first we generali
Externí odkaz:
http://arxiv.org/abs/1704.02010
Autor:
Arya, Sakshi, Abhishek, Anuj
Publikováno v:
Sankhya A; Aug2023, Vol. 85 Issue 2, p1127-1155, 29p