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

A Generalized Methodology for Creating a Taxonomy of Terminology for Any Business Discipline Using Automated Text Analysis

For businesses to function properly and interact with each other in modern supply networks, it is critically important that they have high quality communication processes based on commonly accepted bodies of professional terminology.A taxonomy designed from a set of terms derived empirically by way of textual analysis could serve as a linguistic foundation for the communication process mentioned above.In any organization the professional language based on such terminology exists as a continuous social process of negotiating the meaning for and upholding the accepted use of the old terms as well as the new ones.But, in today\u27s business world, new disciplines and changes to existing disciplines occur so rapidly that it is difficult for practitioners to develop and agree on common sets of terminology quickly enough.This research deals with an issue deemed central to any business, which is the issue of removing the barriers in professional communication and understanding. Specifically we study the means of resolving the problems with the new and confusing terminology aggressively promoted by highly innovative members of industries, both new firms as well as the established industry leaders whose influence cannot be ignored by their customers.The problem is modeled and researched first, after which the research findings are used as guiding principles for a designed solution, which concludes the current research effort.Shannon’s (1948) Communication Model serves as a master model, which ties together all theories, referenced in this research.Following the Design Science paradigm the solution comes in the form of a planned language process, the main feature of which is the evolving taxonomy, which is a designed outcome of computer-assisted textual analysis.While many highly dynamic industries face these challenges, for this study we chose the database industry as highly indicative of the problem, and especially its Big Data products.We pay special attention to clarity in presenting the researcher’s view on research design for this inquiry. This view is based on Crotty (1998) research design elements, which permits both qualitative and quantitative methods to be utilized in our study.Systematics is emphasized throughout the research process

Singular FIOs in SAR Imaging, II: transmitter and receiver at different speeds

In this article, we consider two bistatic cases arising in synthetic aperture radar imaging: when the transmitter and receiver are both moving with different speeds along a single line parallel to the ground in the same direction or in the opposite directions. In both cases, we classify the forward operator F as a Fourier integral operator with fold/blowdown singularities. Next we analyze the normal operator F* F in both cases (where F* is the L-2-adjoint of F). When the transmitter and receiver move in the same direction, we prove that F* F belongs to a class of operators associated to two cleanly intersecting Lagrangians, I-p,I-l (Delta, C-1). When they move in opposite directions, F* F is a sum of such operators. In both cases artifacts appear, and we show that they are, in general, as strong as the bona fide part of the image. Moreover, we demonstrate that as soon as the source and receiver start to move in opposite directions, there is an interesting bifurcation in the type of artifact that appears in the image