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- Yuan Xu, Lihong V. Wang, Gaik Ambartsoumian, Peter Kuchment
- Medical physics
- 2004

The limited-view problem is studied for thermoacoustic tomography, which is also referred to as photoacoustic or optoacoustic tomography depending on the type of radiation for the induction of acoustic waves. We define a "detection region," within which all points have sufficient detection views. It is explained analytically and shown numerically that theâ€¦ (More)

The circular Radon transform integrates a function over the set of all spheres with a given set of centers. The problem of injectivity of this transform (as well as inversion formulas, range descriptions, etc.) arises in many fields from approximation theory to integral geometry, to inverse problems for PDEs, and recently to newly developing types ofâ€¦ (More)

- Gaik Ambartsoumian, Peter Kuchment
- SIAM J. Math. Analysis
- 2006

The transform considered in the paper integrates a function supported in the unit disk on the plane over all circles centered at the boundary of this disk. Such circular Radon transform arises in several contemporary imaging techniques, as well as in other applications. As it is common for transforms of Radon type, its range has infinite codimension inâ€¦ (More)

The representation of a function by its circular Radon transform (CRT) and various related problems arise in many areas of mathematics, physics and imaging science. There has been a substantial spike of interest towards these problems in the last decade mainly due to the connection between the CRT and mathematical models of several emerging medical imagingâ€¦ (More)

- Gaik Ambartsoumian
- Computers & Mathematics with Applications
- 2012

- Britnee A Crawford, Christopher Kribs-Zaleta, Gaik Ambartsoumian
- Bulletin of mathematical biology
- 2013

The parasite Trypanosoma cruzi, known for causing Chagas' disease, is spread via insect vectors from the triatomine family. T. cruzi is maintained in sylvatic vector-host transmission cycles in certain parts of the Americas. Communication between the cycles occurs mainly through movement (migration) of the insect vectors. In this study, we develop aâ€¦ (More)

Exterior inverse problem for the circular means transform (CMT) arises in the intravascular photoacoustic imaging (IVPA), in the intravascular ultrasound imaging (IVUS), as well as in radar and sonar. The reduction of the IPVA to the CMT is quite straightforward. As shown in the paper, in IVUS the circular means can be recovered from measurements by solvingâ€¦ (More)

The circular Radon transform integrates a function over the set of all spheres with a given set of centers. The problem of injectivity of this transform (as well as inversion formulas, range descriptions, etc.) arises in many fields from approximation theory to integral geometry, to inverse problems for PDEs, and recently to newly developing types ofâ€¦ (More)

- Gaik Ambartsoumian, Souvik Roy
- IEEE Transactions on Computational Imaging
- 2016

The article presents an efficient image reconstruction algorithm for single scattering optical tomography (SSOT) in circular geometry of data acquisition. This novel medical imaging modality uses photons of light that scatter once in the body to recover its interior features. The mathematical model of SSOT is based on the broken ray (or V-line Radon)â€¦ (More)

The problem of image reconstruction in thermoacoustic tomography requires inversion of a generalized Radon transform, which integrates the unknown function over circles in 2D or spheres in 3D. The paper investigates implementation of the recently discovered backprojection type inversion formulas for the case of spherical acquisition in 3D. A numericalâ€¦ (More)