title: Fast predictions of variance images for fan-beam transmission tomography with quadratic regularization.
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 [1] 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).
authors.affiliation: Electrical Engineering and Computer Science Department, The University of Michigan, Ann Arbor, MI 48109, USA. yzz@eecs.umich.edu
authors.forename: Yingying
authors.initials: Y
authors.lastname: Zhang-O'Connor
authors.forename: Jeffrey A
authors.initials: JA
authors.lastname: Fessler
mesh_terms: D000465:Algorithms; D005583:Fourier Analysis; D009716:Numerical Analysis, Computer-Assisted; D019047:Phantoms, Imaging; D011856:Radiographic Image Enhancement / Q000379:methods*; D011857:Radiographic Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D013997:Time Factors; D014056:Tomography, X-Ray / Q000295:instrumentation / Q000379:methods*