The reconstruction of fan-beam data by filtering the back-projection

Abstract

Expressions for the fan-beam projection and back-projection operators are given along with an evaluation of the impulse response for the composite of the projection and back-projection operations. The fan-beam geometries for both curved and flat detectors have back-projection operators such that the impulse response for the composite of the projection and backprojection operations is equal to 1/ l.r -r I if the data are taken over 360° 0 and thus two-dimensional Fourier filter techniques can be used to reconstruct transverse sections from fan-beam projection data. It will be shown that the impulse response for the composite of the projection and back-projection operators for fan-beam geometry is not spatially invariant if the data are taken over 180° as is true for parallel-beam projection data. The convolution algorithm is approximately four times faster and requires 40% less memory than the filter of the back-projection algorithm. However, the filter of the backprojection algorithm has the advantage of easily implementing different frequency space filters which lends itself to easily changing the noise propagation vs. resolution properties of the convolution kernel. iii 0 0 : ~ t,.JI 6 0

X-ray computed tomography system for laboratory small-object imaging: Enhanced tomography solutions

“…Due to the system's $ 10°cone-beam angle, this approximation causes some loss of resolution near the edge of the Z-axis field-of-view. The pseudo-parallel fanbeam projections are reconstructed using a fan-to-parallel-beam rebinning algorithm followed by a filtered back-projection algorithm, with a standard ramp filter and filtering function (Pan and Kak, 1983;Miller and Sampath Kumaran, 1982;Gullberg, 1979;Katsevich, 2002). Work is underway to develop image analysis and segmentation algorithms to automatically determine the size and mass of various object components.…”

List-mode data reconstruction via the finite Hilbert transform of the derivative of the backprojection

“…Our proposed method is similar to the reconstruction methods that backproject the image first, then apply a 2D ramp filter [8] [9]. Ideally, if a post 2D ramp filtering method is used, the backprojected image should be available in an unbounded 2D plane.…”

Estimation of geometrical parameters for fan beam tomography

“…The projections of the point source are obtained by substituting equation (1) into the expression for the fan beam projection operator (Gullberg 1979):…”