Inversion for the attenuated radon transform with constant attenuation

Conference · Wed Feb 01 04:00:00 EST 1984 · IEEE Trans. Nucl. Sci.; (United States)

OSTI ID:6671142

Kim, K I; Bizais, Y; Rowe, R W; Tewarson, R P

An exact form of the inversion formula for the attenuated Radon transform with constant attenuation in a convex domain for use in Single-Photon Computerized Tomography is presented. This problem is reduced to solving a generalized Abel integral equation and the conditions for the existence of a unique continuous solution are given. Implementation of this method involves a preprocessing step (modified attenuated Radon transform), a convolution by an attenuation-dependent function and a weighted backprojection. Therefore, only slight modifications of existing reconstruction algorithms are needed. If the attenuation is zero, this formula reduces to Radon's original inversion formula. When attenuation is not constant, the conditions for a unique continuous solution can be established with a similar approach. Many results found empirically by previous authors are consistent with this theory.

• Research Organization: Brookhaven Nat'l. Lab., Upton, NY, and S.U.N.Y. at Stony Brook, NY
• OSTI ID: 6671142
• Report Number(s): CONF-831015-
• Conference Information: Journal Name: IEEE Trans. Nucl. Sci.; (United States) Journal Volume: 31:1
• Country of Publication: United States
• Language: English

Related Subjects

550601* -- Medicine-- Unsealed Radionuclides in Diagnostics
62 RADIOLOGY AND NUCLEAR MEDICINE
ALGORITHMS
ATTENUATION
BACKSCATTERING
COMPUTER CALCULATIONS
COMPUTERIZED TOMOGRAPHY
DIAGNOSTIC TECHNIQUES
EMISSION COMPUTED TOMOGRAPHY
EQUATIONS
FUNCTIONS
IMAGE PROCESSING
INTEGRAL EQUATIONS
MATHEMATICAL LOGIC
MODIFICATIONS
PROCESSING
SCATTERING
SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY
TOMOGRAPHY
TRANSFORMATIONS
WEIGHTING FUNCTIONS