Range descriptions for the spherical mean Radon transform Academic Article

abstract

• The transform considered in the paper averages a function supported in a ball in Rn over all spheres centered at the boundary of the ball. This Radon type transform arises in several contemporary applications, e.g. in thermoacoustic tomography and sonar and radar imaging. Range descriptions for such transforms are important in all these areas, for instance when dealing with incomplete data, error correction, and other issues. Four different types of complete range descriptions are provided, some of which also suggest inversion procedures. Necessity of three of these (appropriately formulated) conditions holds also in general domains, while the complete discussion of the case of general domains would require another publication. 2007 Elsevier Inc. All rights reserved.

authors

• Kuchment, Peter

published proceedings

• JOURNAL OF FUNCTIONAL ANALYSIS

author list (cited authors)

• Agranovsky, M., Kuchment, P., & Quinto, E. T.

citation count

• 50

complete list of authors

• Agranovsky, Mark||Kuchment, Peter||Quinto, Eric Todd

publication date

• July 2007

publisher

• Elsevier  Publisher

published in

• Journal of Functional Analysis  Journal

keywords

• Darboux Equation
• Inversion
• Radon Transforms
• Range
• Spherical Mean Operators
• Tomography

Digital Object Identifier (DOI)

• 10.1016/j.jfa.2007.03.022

start page

• 344

end page

• 386

volume

• 248

issue

• 2

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.jfa.2007.03.022