Determining a Function from Its Mean Values Over a Family of Spheres
By David V. Finch, Sarah K. Patch, Rakesh. SIAM Journal on Mathematical Analysis, 2004
456 citations recorded by the source corpus.
Subfields: Computational Mechanics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/02c1aef69f0951555aebbac1d8171661f8ec3c89
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Mechanics
- Markus Haltmeier
- G. Paltauf
- Peter Burgholzer
- Otmar Scherzer
- Simon Robert Arridge
- Leonid A. Kunyansky
- Peter Kuchment
- Peter Maass
In Computational Theory and Mathematics
- Markus Haltmeier
- G. Paltauf
- Peter Burgholzer
- Leonid A. Kunyansky
- Peter Kuchment
- Simon Robert Arridge
- Otmar Scherzer
In Mathematical Physics
- Leonid A. Kunyansky
- Peter Kuchment
- Markus Haltmeier
- G. Paltauf
- Peter Burgholzer
- Otmar Scherzer
- Simon Robert Arridge
- Konstantin Pankrashkin
Citations in the corpus
- Experimental evaluation of reconstruction algorithms for limited view photoacoustic tomography with line detectors (2007, unknown): “In the more established imaging procedures employing small point-like detectors the signals at a given time are related to the spherical Radon transform, consisting of integrals of the energy density distribution over spherical surfaces [1, 5–7].”
- Reconstructive Integral Geometry (2004, background): “10 [22]If n ≥ 3 is odd, then for any contunous function f and point x ∈ B we have”
- Mathematics of thermoacoustic tomography (2007, background): “In the constant speed case, the following approach is possible in 3D [38]: due to the validity of the Huygens’ principle (i.”
- Thermoacoustic computed tomography with large planar receivers (2004, methodology): “In the literature, analytical formulas for calculating the density function from measurement data of the pressure have been derived for various sample geometries, such as planes, spheres, cylinders, and circles [4, 15, 16, 17, 9, 10, 8].”
- Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems (2012, unknown): “[51] D. Finch, S.K Patch and Rakesh, Determining a function from its mean values over a family of spheres, SIAM J. Math.”
- Temporal back-projection algorithms for photoacoustic tomography with integrating line detectors (2007, methodology): “The first exact BP formulae in three dimensions were derived for a spherical detection surface [18, 19, 35] and in two dimensions for a circular detection curve [35, 36].”
- Quantitative spectroscopic photoacoustic imaging: a review. (2012, background): “(1) and (6) gives an expression for the initial pressure distribution as”
- Inversion of Spherical Means and the Wave Equation in Even Dimensions (2007, background): “(1.12)”