dorsal/arxiv
View SchemaReconstruction Algorithms for Positron Emission Tomography and Single Photon Emission Computed Tomography and their Numerical Implementation
| Authors | A. S. Fokas, A. Iserles, V. Marinakis |
|---|---|
| Categories | |
| ArXiv ID | physics/0412030 |
| URL | https://arxiv.org/abs/physics/0412030 |
Abstract
The modern imaging techniques of Positron Emission Tomography and of Single Photon Emission Computed Tomography are not only two of the most important tools for studying the functional characteristics of the brain, but they now also play a vital role in several areas of clinical medicine, including neurology, oncology and cardiology. The basic mathematical problems associated with these techniques are the construction of the inverse of the Radon transform and of the inverse of the so called attenuated Radon transform respectively. We first show that, by employing mathematical techniques developed in the theory of nonlinear integrable equations, it is possible to obtain analytic formulas for these two inverse transforms. We then present algorithms for the numerical implementation of these analytic formulas, based on approximating the given data in terms of cubic splines. Several numerical tests are presented which suggest that our algorithms are capable of producing accurate reconstruction for realistic phantoms such as the well known Shepp--Logan phantom.
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"abstract": "The modern imaging techniques of Positron Emission Tomography and of Single\nPhoton Emission Computed Tomography are not only two of the most important\ntools for studying the functional characteristics of the brain, but they now\nalso play a vital role in several areas of clinical medicine, including\nneurology, oncology and cardiology. The basic mathematical problems associated\nwith these techniques are the construction of the inverse of the Radon\ntransform and of the inverse of the so called attenuated Radon transform\nrespectively. We first show that, by employing mathematical techniques\ndeveloped in the theory of nonlinear integrable equations, it is possible to\nobtain analytic formulas for these two inverse transforms. We then present\nalgorithms for the numerical implementation of these analytic formulas, based\non approximating the given data in terms of cubic splines. Several numerical\ntests are presented which suggest that our algorithms are capable of producing\naccurate reconstruction for realistic phantoms such as the well known\nShepp--Logan phantom.",
"arxiv_id": "physics/0412030",
"authors": [
"A. S. Fokas",
"A. Iserles",
"V. Marinakis"
],
"categories": [
"physics.med-ph",
"math.NA"
],
"title": "Reconstruction Algorithms for Positron Emission Tomography and Single Photon Emission Computed Tomography and their Numerical Implementation",
"url": "https://arxiv.org/abs/physics/0412030"
},
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