Linear analysis of rotationally invariant, radially variant tomographic imaging systems

Conference · Mon Jan 01 04:00:00 EST 1990

DOI:https://doi.org/10.1117/12.18820· OSTI ID:7008359

Baker, J R; Budinger, T F; Huesman, R H ^[1]

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1. Lawrence Berkeley Lab., CA (USA)

We describe a method to analyze the linear imaging characteristics of rotationally invariant, radially variant tomographic imaging systems using singular value decomposition (SVD). When the projection measurements from such a sysem are assumed to be samples from independent and identically distributed multi-normal random variables, the best estimate of the emission intensity is given by the unweighted lease squares estimator. The noise amplification of this estimator is inversely proportional to the singular values of the normal matrix used to model projection and backprojection. After choosing an acceptable noise amplification, the new method can determine the number of parameters and hence the number of pixels that should be estimated from data acquired from an existing system with a fixed number of angles and projection bins. Conversely, for the design of a new system, the number of angles and projection bins necessary for a given number of pixels and noise amplification can be determined. In general, computing the SVD of the projection normal matrix for this class of rotationally invariant, radially variant systems has a block circulant form. A fast parallel algorithm to compute the SVD of this block circulant matrix makes the singular value analysis practical by asymptotically reducing the computation complexity of the method by a multiplicative factor equal to the number of angles squared. 11 refs.

• Research Organization: Lawrence Berkeley Lab., CA (USA)
• Sponsoring Organization: DOE/ER; DOHHS
• DOE Contract Number: AC03-76SF00098
• OSTI ID: 7008359
• Report Number(s): LBL-28764; CONF-900238--3; ON: DE90011607
• Country of Publication: United States
• Language: English

Related Subjects

550602* -- Medicine-- External Radiation in Diagnostics-- (1980-)
62 RADIOLOGY AND NUCLEAR MEDICINE
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
AMPLIFICATION
CHEMICAL REACTIONS
COMPUTERIZED TOMOGRAPHY
DATA ACQUISITION
DECOMPOSITION
DIAGNOSTIC TECHNIQUES
EIGENFUNCTIONS
FOURIER TRANSFORMATION
FUNCTIONS
IMAGE PROCESSING
INTEGRAL TRANSFORMATIONS
MATHEMATICAL MODELS
NOISE
PERFORMANCE
PROCESSING
TOMOGRAPHY
TRANSFORMATIONS