Date

2018

Major

Mathematics (B.S.)

Document Type and Release Option

Thesis (open access)

Faculty Mentor

Jiehua Zhu

Abstract

Area based projection models for computed tomography mitigate raw data errors by treating X-Rays as beams, whereas traditional line based projection models treat an X-Ray like a line, thus generating significant error. In an existing area based fan beam projection model, a rotation matrix, Q, simulates the rotation of the emitter detector pair to reduce computational load, but this introduces approximations by using an approximated rotation matrix. We eliminate approximations by deriving an exact formula for the entries of Q. Using a rotation of axes and by considering the neighboring cells' contributions to the area, the result has formulations for the exact calculation of the matrix Q. Thus, approximations are phased out, and error in projection data is minimized for image reconstruction.

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