arXiv subjects

Gaik Ambartsoumian

Publications and source records attributed to Gaik Ambartsoumian.

21 records · Page 2Linked to original sources

arXiv2005

Thermoacoustic tomography - implementation of exact backprojection formulas

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 numerical simulation of the data acquisition with subsequent reconstructions are made for the Defrise phantom as well as for some other phantoms. Both full and partial scan situations are considered. The results are compared with the implementation of a previously used approximate inversion formula.

math.NA↗

arXiv2005

A range description for the planar circular Radon transform

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 co-dimension in standard function spaces. Range descriptions for such transforms are known to be very important for computed tomography, for instance when dealing with incomplete data, error correction, and other issues. A complete range description for the circular Radon transform is obtained. Range conditions include the recently found set of moment type conditions, which happens to be incomplete, as well as the rest of conditions that have less standard form. In order to explain the procedure better, a similar (non-standard) treatment of the range conditions is described first for the usual Radon transform on the plane.

math.GM↗

arXiv2004

On the injectivity of the circular Radon transform arising in thermoacoustic tomography

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 of tomography. The article discusses known and provides new results that one can obtain by methods that essentially involve only the finite speed of propagation and domain dependence for the wave equation.

math-ph↗