Fast predictions of variance images for fan-beam transmission tomography with quadratic regularization.

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.

Fourier-based forward and back-projectors in iterative fan-beam tomographic image reconstruction.

Fourier-based forward and back-projection methods can reduce computation in iterative tomographic image reconstruction. Recently, an optimized nonuniform fast Fourier transform (NUFFT) approach was shown to yield accurate parallel-beam projections. In this paper, we extend the NUFFT approach to describe an O (N2 log N) projector/backprojector pair for fan-beam transmission tomography.