A reconstruction algorithm using singular value decomposition of a discrete representation of the exponential Radon transform using natural pixels

Conference · Thu Dec 01 04:00:00 EST 1994 · IEEE Transactions on Nuclear Science (Institute of Electrical and Electronics Engineers); (United States)

OSTI ID:6700262

Gullberg, G T; Zeng, G L ^[1]

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1. Univ. of Utah, Salt Lake City, UT (United States). Dept. of Radiology

An algorithm to correct for constant attenuation in SPECT is derived from the singular value decomposition (SVD) of a discrete representation of the exponential Radon transform using natural pixels. The algorithm is based on the assumption that a continuous image can be obtained by backprojecting the discrete array q, which is the least squares solution to Mq = p, where p is the array of discrete measurements, and the matrix M represents the composite operator of the backprojection operator A*[sub [mu]] followed by the projection operator A[sub [mu]]. A singular value decomposition of M is used to solve the equation Mq = p, and the final image is obtained by sampling the backprojection of the solution q at a discrete array of points. Analytical expressions are given to calculate the matrix elements of M that are integrals of exponential factors over the overlapped area of two projection strip functions (natural pixels). A spectral analysis of the exponential Radon transform is compared with that of the Radon transform. The condition number of the spectrum increases with increased attenuation coefficient, which correlates with the increase in statistical error propagation seen in clinical images obtained with low-energy radionuclides. Computer simulations using 32 projections sampled over 360 degrees show an improvement in the SVD reconstruction over the convolution backprojection reconstruction, especially when the projection data is corrupted with noise.

• OSTI ID: 6700262
• Report Number(s): CONF-931051--
• Conference Information: Journal Name: IEEE Transactions on Nuclear Science (Institute of Electrical and Electronics Engineers); (United States) Journal Volume: 41:6Pt2
• Country of Publication: United States
• Language: English

Related Subjects

550601* -- Medicine-- Unsealed Radionuclides in Diagnostics
62 RADIOLOGY AND NUCLEAR MEDICINE
ACCURACY
ALGORITHMS
ATTENUATION
COMPUTERIZED TOMOGRAPHY
DIAGNOSTIC TECHNIQUES
EMISSION COMPUTED TOMOGRAPHY
IMAGE PROCESSING
LEAST SQUARE FIT
MATHEMATICAL LOGIC
MAXIMUM-LIKELIHOOD FIT
NUMERICAL SOLUTION
PROCESSING
SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY
TOMOGRAPHY