F. John's Ultrahyperbolic Equation and 3D Computed Tomography

Friday, September 28, 2001 - 10:10am - 12:00pm
Vincent 570
Sarah Patch (General Electric Corp., Research and Development Center)
Computed Tomography (CT or CAT-scan) data is simply line integrals of the object being imaged. In the plane, the dimension count of the data and reconstructed are equal. In higher dimensions, however, the data space is much larger than the image space. Measured data for 3D CT, therefore, is subject to consistency conditions described by ultrahyperbolic equations

Typical clinical CT systems measure line integrals on a characteristic surface for John's equation. By solving this BV problem we convert the 3D CT reconstruction problem into the 2D reconstruction problem (that CT systems have been reconstructing for 25 years!)