DocumentCode :
1191391
Title :
Fast Predictions of Variance Images for Fan-Beam Transmission Tomography With Quadratic Regularization
Author :
Yingying Zhang-O´Connor ; Fessler, Jeffrey A.
Author_Institution :
Electr. Eng. & Comput. Sci. Dept., Michigan Univ., Ann Arbor, MI
Volume :
26
Issue :
3
fYear :
2007
fDate :
3/1/2007 12:00:00 AM
Firstpage :
335
Lastpage :
346
Abstract :
Accurate predictions of image variances can be useful for reconstruction algorithm analysis and for the design of regularization methods. Computing the predicted variance at every pixel using matrix-based approximations is impractical. Even most recently adopted methods that are based on local discrete Fourier approximations are impractical since they would require a forward and backprojection and two fast Fourier transform (FFT) calculations for every pixel, particularly for shift-variant systems like fan-beam tomography. This paper describes new "analytical" approaches to predicting the approximate variance maps of 2-D images that are reconstructed by penalized-likelihood estimation with quadratic regularization in fan-beam geometries. The simplest of the proposed analytical approaches requires computation equivalent to one backprojection and some summations, so it is computationally practical even for the data sizes in X-ray computed tomography (CT). Simulation results show that it gives accurate predictions of the variance maps. The parallel-beam geometry is a simple special case of the fan-beam analysis. The analysis is also applicable to 2-D positron emission tomography (PET)
Keywords :
computerised tomography; estimation theory; image reconstruction; medical image processing; 2-D positron emission tomography; X-ray computed tomography; fan-beam geometries; fan-beam transmission tomography; penalized-likelihood estimation; quadratic regularization; reconstruction algorithm; regularization methods; variance images; Algorithm design and analysis; Analysis of variance; Computed tomography; Design methodology; Fast Fourier transforms; Geometry; Image analysis; Positron emission tomography; Reconstruction algorithms; X-ray imaging; Fan-beam tomography; local discrete Fourier analysis; penalized-likelihood image reconstruction; variance approximation; Algorithms; Fourier Analysis; Numerical Analysis, Computer-Assisted; Phantoms, Imaging; Radiographic Image Enhancement; Radiographic Image Interpretation, Computer-Assisted; Reproducibility of Results; Sensitivity and Specificity; Signal Processing, Computer-Assisted; Time Factors; Tomography, X-Ray;
fLanguage :
English
Journal_Title :
Medical Imaging, IEEE Transactions on
Publisher :
ieee
ISSN :
0278-0062
Type :
jour
DOI :
10.1109/TMI.2006.887368
Filename :
4114562
Link To Document :
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