Guy M. Besson

CT image reconstruction from fan‐parallel data

Third generation fan-beam computerized tomography(CT) 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 fan-parallel 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.

CT projection estimation and applications to fast and local reconstruction

In this paper, a straightforward method of estimating the CT projections is applied to simplified pre-processing, simplified reconstruction filtering, and to low-dose and local CT image reconstruction. The method relies on the projection- to-projection data redundancy that is shown to exist in CT. In the pre-processing application, the output of a few, angularly sparse fully pre-processed projections, is utilized in a linearization model to estimate directly the output of pre- processing for all the other projections. In the reconstruction filtering application, and with projection i and k being fully filtered, intermediate projection j low frequency components are estimated by a linear combination of projections i and k. That estimate is then subtracted from projection j, and the resulting high-frequency components are then filtered without zeropadding. By linearity the same combination of fully filtered projections i and k is added back to projection j. A factor two simplification is obtained, that can be leveraged for reconstruction speed or cost reduction. The local reconstruction application builds on the filtering method, by showing that truncated data is sufficient for calculating a filtered projection high-frequencies, while a very simple projection completion model is shown to be effective in estimating the low frequencies. Image quality comparisons are described.

A z gain nonuniformity correction for multislice volumetric CT scanners.

This paper presents a calibration and correction method for detector cell gain variations. A key functionality of current CT scanners is to offer variable slice thickness to the user. To provide this capability in multislice volumetric scanners, while minimizing costs, it is necessary to combine the signals of several detector cells in z, when the desired slice thickness is larger than the minimum provided by a single cell. These combined signals are then pre-amplified, digitized, and transmitted to the system for further processing. The process of combining the output of several detector cells with nonuniform gains can introduce numerical errors when the impinging x-ray signal presents a variation along z over the range of combined cells. These numerical errors, which by nature are scan dependent, can lead to artifacts in the reconstructed images, particularly when the numerical errors vary from channel-to-channel (as the filtered-backprojection filter includes a high-pass filtering along the channel direction, within a given slice). A projection data correction algorithm has been developed to subtract the associated numerical errors. It relies on the ability of calibrating the individual cell gains. For effectiveness and data flow reasons, the algorithm works on a single slice basis, without slice-to-slice exchange of information. An initial error vector is calculated by applying a high-pass filter to the projection data. The essence of the algorithm is to correlate that initial error vector, with a calibration vector obtained by applying the same high-pass filter to various z combinations of the cell gains (each combination representing a basis function for a z expansion). The solution of the least-square problem, obtained via singular value decomposition, gives the coefficients of a polynomial expansion of the signal z slope and curvature. From this information, and given the cell gains, the final error vector is calculated and subtracted from the projection data.

Algorithm to correct for z-detector gain variations in multislice volumetric CT

This paper presents a calibration and correction method for detector cell gain variations. To provide variable slice thickness capability in multislice volumetric scanners, while minimizing costs, it is necessary to combine the signals from several detector cells. The process of combining the output of several detector cells with non-uniform gains can introduce numerical errors when the impinging x-ray signal varies over the range of the combined cells. These scan dependent numerical errors can lead to artifacts in the reconstructed images, particularly when the numerical errors vary from channel-to-channel. A projection data correction algorithm has been developed to subtract the associated numerical errors. For effectiveness and data flow reasons, the algorithm works on a slice-by-slice basis. An initial error vector is calculated by applying a high-pass filter to the projection data. The essence of the algorithm is to correlate that initial error vector, with a calibration vector obtained by applying the same high-pass filter to various z-combinations of the cell gains. The solution to the least-square problem gives the coefficients of a polynomial expansion of the signal z-slope and curvature. From this information, and given the cell gains, the final error vector is calculated and subtracted from the projection data.