Cone beam local tomography
Abbreviated Journal Title
SIAM J. Appl. Math.
spiral CT; cone-beam data; local tomography; pseudodifferential; operators; singularities; artifacts; X-RAY TRANSFORM; SUFFICIENT CONDITIONS; RECONSTRUCTION; ALGORITHM; Mathematics, Applied
In this paper we study three-dimensional cone beam local tomography. We analyze the local tomography function f(Lambda)(c), which was proposed earlier in [A.K. Louis and P. Maass, IEEE Trans. Medical Imaging, 12 (1993), pp. 764-769]. Let f be an unknown density distribution inside an object being scanned. We find a relationship between the wave fronts of f(Lambda)(c) and f and compute the principal symbol of the operator which maps f into f(Lambda)(c). Our results prove the fact, which was first noted in Louis and Maass, that one can recover most of the singularities of f knowing f(Lambda)(c). It is shown that these are precisely the singularities of f that are visible from the data. A simple and efficient algorithm for finding values of jumps of f knowing local cone beam data is proposed. The nature of artifacts inherent in cone beam local tomography is studied.
Siam Journal on Applied Mathematics
"Cone beam local tomography" (1999). Faculty Bibliography 1990s. 2692.