A Radon-type transform arising in photoacoustic tomography with circular detectors
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Sunghwan Moon
Abstract
Photoacoustic tomography is the most well-known example of a hybrid imaging method. In this article, we define a Radon-type transform arising in a version of photoacoustic tomography that uses integrating circular detectors and describe how the Radon transform integrating over all circles with a fixed radius is determined from this Radon-type transform. We consider three situations in which the centers of the circular detectors are located on a cylinder, on a plane, and on a sphere. This transform is similar to a toroidal Radon transform, which maps a given function to its integrals over a set of tori. We also study this object.
Funding source: NSF
Award Identifier / Grant number: DMS 0908208
Funding source: NSF
Award Identifier / Grant number: DMS 1211463
Funding statement: This work was partly supported by NSF grants DMS 0908208 and DMS 1211463.
The author thanks P. Kuchment and D. Steinhauer for fruitful discussions.
© 2016 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Inverse scattering problem for the nonstationary Dirac equation on the half-plane
- A Radon-type transform arising in photoacoustic tomography with circular detectors
- Recovery of the matrix quadratic differential pencil from the spectral data
- The effect of resonance on the linear sampling method
- Inverse problems for parabolic equations with interior degeneracy and Neumann boundary conditions
- Incorporating a posteriori error estimators in an adaptive parametrization algorithm
- Generalized sensitivity functions for size-structured population models
- Stable gradient projection method for nonlinear conditionally well-posed inverse problems
- Uniqueness and non-uniqueness in acoustic tomography of moving fluid
- Convex Tikhonov regularization in Banach spaces: New results on convergence rates
- Calderón problem for Maxwell's equations in two dimensions
Artikel in diesem Heft
- Frontmatter
- Inverse scattering problem for the nonstationary Dirac equation on the half-plane
- A Radon-type transform arising in photoacoustic tomography with circular detectors
- Recovery of the matrix quadratic differential pencil from the spectral data
- The effect of resonance on the linear sampling method
- Inverse problems for parabolic equations with interior degeneracy and Neumann boundary conditions
- Incorporating a posteriori error estimators in an adaptive parametrization algorithm
- Generalized sensitivity functions for size-structured population models
- Stable gradient projection method for nonlinear conditionally well-posed inverse problems
- Uniqueness and non-uniqueness in acoustic tomography of moving fluid
- Convex Tikhonov regularization in Banach spaces: New results on convergence rates
- Calderón problem for Maxwell's equations in two dimensions
