13 citations · 28 across the 17 of their papers we have counts for
17 papers
On a quantitative partial imaging problem in vector tomography
Hiroshi Fujiwara, Kamran Sadiq, Alexandru Tamasan
In two dimensions, we consider the problem of reconstructing a vector field from partial knowledge of its zeroth and first moment ray transforms. Different from existing works the…
Computational inverse scattering with internal sources: a reproducing kernel Hilbert space approach
Yakun Dong, Kamran Sadiq, Otmar Scherzer +1
We present a method to reconstruct the dielectric susceptibility (scattering potential) of an inhomogeneous scattering medium, based on the solution to the inverse scattering probl…
Inversion of the attenuated momenta ray transform of planar symmetric tensors
Hiroshi Fujiwara, David Omogbhe, Kamran Sadiq +1
We present a reconstruction method that stably recovers the real valued, symmetric tensors compactly supported in the Euclidean plane, from knowledge of their attenuated momenta ra…
Inversion of the Momenta Doppler Transform in two dimensions
Hiroshi Fujiwara, David Omogbhe, Kamran Sadiq +1
We introduce an analytic method which stably reconstructs both components of a (sufficiently) smooth, real valued, vector field compactly supported in the plane from knowledge of i…
An inverse source problem for linearly anisotropic radiative sources in absorbing and scattering medium
David Omogbhe, Kamran Sadiq
We consider in a two dimensional absorbing and scattering medium, an inverse source problem in the stationary radiative transport, where the source is linearly anisotropic. The med…
On the -ray transform of symmetric higher order tensors
David Omogbhe, Kamran Sadiq
In this article we characterize the range of the attenuated and non-attenuated -ray transform of compactly supported symmetric tensor fields in the Euclidean plane. The characte…
On the range of the -ray transform of symmetric tensors compactly supported in the plane
Kamran Sadiq, Alexandru Tamasan
We find the necessary and sufficient conditions on the Fourier coefficients of a function on the torus to be in the range of the -ray transform of a symmetric tensor of comp…
Numerical reconstruction of radiative sources from partial boundary measurements
Hiroshi Fujiwara, Kamran Sadiq, Alexandru Tamasan
We consider an inverse source problem in the stationary radiative transport through an absorbing and scattering medium in two dimensions. Using the angularly resolved radiation mea…
On the range of the planar -ray transform on the Fourier lattice of the torus
Kamran Sadiq, Alexandru Tamasan
We find necessary and sufficient conditions on the Fourier coefficients of a function on the torus to be in the range of the -ray transform of functions with compact support…
A source reconstruction method in two dimensional radiative transport using boundary data measured on an arc
Hiroshi Fujiwara, Kamran Sadiq, Alexandru Tamasan
We consider an inverse source problem in the stationary radiating transport through a two dimensional absorbing and scattering medium. Of specific interest, the exiting radiation i…
Inverse Problems of Single Molecule Localization Microscopy
Montse Lopez-Martinez, Gwenael Mercier, Kamran Sadiq +5
Single molecule localization microscopy is a recently developed superresolution imaging technique to visualize structural properties of single cells. The basic principle consists i…
Numerical reconstruction of radiative sources in an absorbing and non-diffusing scattering medium in two dimensions
Hiroshi Fujiwara, Kamran Sadiq, Alexandru Tamasan
We consider the two dimensional quantitative imaging problem of recovering a radiative source inside an absorbing and scattering medium from knowledge of the outgoing radiation mea…
A Fourier approach to the inverse source problem in an absorbing and anisotropic scattering medium
Hiroshi Fujiwara, Kamran Sadiq, Alexandru Tamasan
We revisit the inverse source problem in a two dimensional absorbing and scattering medium and present a non-iterative reconstruction method using measurements of the radiating flu…
Partial inversion of the 2D attenuated -ray transform with data on an arc
Hiroshi Fujiwara, Kamran Sadiq, Alexandru Tamasan
In two dimensions, we consider the problem of inversion of the attenuated -ray transform of a compactly supported function from data restricted to lines leaning on a given arc.…
Quantitative Photoacoustic Imaging in the Acoustic Regime using SPIM
Alexander Beigl, Peter Elbau, Kamran Sadiq +1
While in standard photoacoustic imaging the propagation of sound waves is modeled by the standard wave equation, our approach is based on a generalized wave equation with variable…
On the Range Characterization of the two dimensional attenuated Doppler Transform
Kamran Sadiq, Alexandru Tamasan
We characterize the range of the attenuated and non-attenuated -ray transform of compactly supported vector fields in the plane. The characterization is in terms of a Hilbert tr…
On the Range of the Attenuated Radon Transform in Strictly Convex Sets
Kamran Sadiq, Alexandru Tamasan
We present new necessary and sufficient conditions for a function on to be in the range of the attenuated Radon transform of a sufficiently smooth function su…