Numerical Inversion of a Broken Ray Transform Arising in Single Scattering Optical Tomography
Abstract of Numerical Inversion of a Broken Ray Transform Arising in Single
Numerical Inversion of a Broken Ray Transform Arising in Single Scattering Optical Tomography.The article presents an efficient image reconstruction algorithm for single scattering optical tomography (SSOT) in circular geometry of data acquisition. This novel medical imaging modality uses photons of light that scatter once in the body to recover its interior features. The mathematical model of SSOT is based on the broken ray (or V-line Radon) transform (BRT), which puts into correspondence to an image function its integrals along V-shaped piecewise linear trajectories. The process of image reconstruction in SSOT requires inversion of that transform. We implement numerical inversion of a broken ray transform in a disc with partial radial data. Our method is based on a relation between the Fourier coefficients of the image function and those of its BRT recently discovered by Ambartsoumian and Moon.
Conclusion
We have developed a numerical algorithm for inversion of the broken ray transform in a disk from radially partial data. Our algorithm uses half of the data that the previously known numerical inversions of BRT in the disc used. Given the limitations on the distance that a photon can fly without scattering more than once, our approach allows to double the thickness of objects that can be imaged using single scattering optical tomography.
