27 research outputs found
A series solution and a fast algorithm for the inversion of the spherical mean Radon transform
An explicit series solution is proposed for the inversion of the spherical
mean Radon transform. Such an inversion is required in problems of thermo- and
photo- acoustic tomography. Closed-form inversion formulae are currently known
only for the case when the centers of the integration spheres lie on a sphere
surrounding the support of the unknown function, or on certain unbounded
surfaces. Our approach results in an explicit series solution for any closed
measuring surface surrounding a region for which the eigenfunctions of the
Dirichlet Laplacian are explicitly known - such as, for example, cube, finite
cylinder, half-sphere etc. In addition, we present a fast reconstruction
algorithm applicable in the case when the detectors (the centers of the
integration spheres) lie on a surface of a cube. This algorithm reconsrtucts
3-D images thousands times faster than backprojection-type methods
A mathematical model and inversion procedure for Magneto-Acousto-Electric Tomography (MAET)
Magneto-Acousto-Electric Tomography (MAET), also known as the Lorentz force
or Hall effect tomography, is a novel hybrid modality designed to be a
high-resolution alternative to the unstable Electrical Impedance Tomography. In
the present paper we analyze existing mathematical models of this method, and
propose a general procedure for solving the inverse problem associated with
MAET. It consists in applying to the data one of the algorithms of
Thermo-Acoustic tomography, followed by solving the Neumann problem for the
Laplace equation and the Poisson equation.
For the particular case when the region of interest is a cube, we present an
explicit series solution resulting in a fast reconstruction algorithm. As we
show, both analytically and numerically, MAET is a stable technique yilelding
high-resolution images even in the presence of significant noise in the data
Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra
We present explicit filtration/backprojection-type formulae for the inversion
of the spherical (circular) mean transform with the centers lying on the
boundary of some polyhedra (or polygons, in 2D). The formulae are derived using
the double layer potentials for the wave equation, for the domains with certain
symmetries. The formulae are valid for a rectangle and certain triangles in 2D,
and for a cuboid, certain right prisms and a certain pyramid in 3D. All the
present inversion formulae yield exact reconstruction within the domain
surrounded by the acquisition surface even in the presence of exterior sources.Comment: 9 figure
Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography
The paper contains a simple approach to reconstruction in Thermoacoustic and
Photoacoustic Tomography. The technique works for any geometry of point
detectors placement and for variable sound speed satisfying a non-trapping
condition. A uniqueness of reconstruction result is also obtained
Ultraviolet Passbands for a Space Multicolor Photometric System
The results of search for the optimal location of ultraviolet passbands for an extra-atmospheric photometric system are given. The addition of passbands near the well-known extinction bump at 218 nm to the photometric system makes it possible to determine interstellar extinction with greater precision than with the photometric system without UV passbands