Linear analysis of rotationally invariant, radially variant tomographic imaging systems

John Robert Baker; Ronald H. Huesman; Thomas F. Budinger

doi:10.1117/12.18820

1 July 1990 Linear analysis of rotationally invariant, radially variant tomographic imaging systems

John Robert Baker, Ronald H. Huesman, Thomas F. Budinger

Proceedings Volume 1231, Medical Imaging IV: Image Formation; (1990) https://doi.org/10.1117/12.18820
Event: Medical Imaging '90, 1990, Newport Beach, CA, United States

Abstract

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 system 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 least 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 arid 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 has cubic computational complexity. However, 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.

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John Robert Baker, Ronald H. Huesman, and Thomas F. Budinger "Linear analysis of rotationally invariant, radially variant tomographic imaging systems", Proc. SPIE 1231, Medical Imaging IV: Image Formation, (1 July 1990); https://doi.org/10.1117/12.18820

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KEYWORDS

Imaging systems

Tomography

Image acquisition

Medical imaging

Computing systems

Statistical analysis

Error analysis

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