CT image reconstruction from fan‐parallel data

Abstract

Third generation fan-beam computerized tomography ͑CT͒ scanners acquire data one entire projection at a time. The associated filtered-backprojection algorithm requires a computationally expensive pixel-dependent weight factor in the backprojector. Methods of simplifying the reconstruction include rebinning the fan-beam data to parallel projections. The rebinning can be separated into two steps: azimuthal interpolation, leading to the fan-parallel geometry, where data are unevenly spaced on radial lines through the origin of Radon space, and a subsequent axial interpolation to parallel data. Under appropriate view and projection sampling conditions, the azimuthal interpolation can be replaced by either data resorting or projection channel-dependent delays. This article investigates an arcsin algorithm to reconstruct an image directly from the fan-parallel data. Although it is shown that the algorithm cannot be exact, a natural approximation is described. The pre-and postconvolution weights, and the reconstruction filter, are derived analytically. Imaging results demonstrate that arcsin image quality matches that of parallel reconstruction. The fanparallel reconstruction method eliminates the resolution-compromising axial interpolation and the costly pixel-dependent backprojection weight. Further, an arcsin detector design is proposed for direct parallel reconstruction from fan-beam data. © 1999 American Association of Physicists in Medicine. ͓S0094-2405͑99͒00403-4͔

The noise power spectrum in CT with direct fan beam reconstruction

“…19 and 20 and several approaches to reduce the nonstationarity were proposed in Refs. [21][22][23]. The NPS of a cone beam CT system was studied in Refs.…”

Improvement of efficiency and flexibility in multi-slice helical CT

“…In order to maintain image quality, the rebinning in the proposed method is different from that given by Ref. [17]. Not only the data p(β i , γ j ) but the interpolated data p d (β 1,z=z0 (n), γ j , n) are used for the linear interpolation for g(θ l , t j ) as given by…”

“…(4) and (5), we can perform rebinning from sampled fan-beam projections p(β i , γ j ) to parallel projections. In general, the rebinning process can be separated into the following two steps: first, data are interpolated in the azimuth to obtain samples on radial lines that are arranged at equiangular intervals [17] ; second, a radial interpolation is performed to obtain equidistant samples on the radial lines. Let β 1,z=z0 (n) and β 2,z=z0 (γ j , n) be, respectively, the view angles when z d (β, n) and z c (β, γ j , n) equal to z 0 , and g(θ l , t j ) be the equiangular sampled parallel projections, where t j corresponds to γ j by Eq.…”

An alternative solution to the nonuniform noise propagation problem in fan‐beam FBP image reconstruction

“…(8) reflects a nonuniform variance distribution across the FOV and this is believed due to the 1/L 2 term in the fFBP of Eq. (5) [3][4][5]. A solution was given by the use of shift-variant filtering in the frequency space to address the non-uniform variance distribution [6].…”

“…The altered noise property from data to image would have an impact on clinical assessment [3], especially for quantitative regional analysis across the FOV. The observed non-uniform noise distribution in the reconstructed image from stationary noisy data is believed to be caused by the distance-dependent 1/L 2 factor in the fFBP reconstruction formula [3][4][5]. Pan et al [6] proposed a solution by a shift-variant means in the filtering step, while retaining the use of spatially-invariant linear interpolation in the backprojection step in the fFBP image reconstruction.…”