Search

In backprojection cone-beam CT the cone-beam projection images are first filtered, then 3D backprojected into the object space. In this paper the point spread function (PSF) for the filtering operation is studied. For the cases where the normalization matrix is a constant, i.e. all integration planes intersect the scan path the same number of times, the derivation of the PSF is extended to the general case of limited angular range for the Radon line integrals. It is found that the 2D component of the PSF can be reduced to the form of space-variant 1D Hilbert transforms. The application of the PSF to a number of aspects in long object imaging will be discussed.

A recent comparison study showed that exact filtered backprojection (FBP)-based solutions of the long object problem are numerically stable and that their image quality is mostly affected by filter design. In this paper, the impact of the kernel design on image quality is demonstrated systematically in the case of the local region-of-interest (ROI) algorithm. First of all, the implementation is improved by the use of the Linogram technique to eliminate interpolations in the filter step and to speed up computation. In the case of the local ROI method, favorable kernels for one-dimensional (1-D) partial derivatives have to be designed. Finite differences are fast to compute but cause ringing artifacts. More sophisticated kernels can be designed in a straightforward manner in Fourier space, identifying the window function most appropriate to a given application. No ringing artifacts are observed for the windowed kernels under investigation. In addition, windowed kernels are superior to the finite differences regarding the spatial resolution versus noise properties. For partial derivatives in directions with data truncation the projection data have to be extrapolated before convolution. Alternatively, very short derivative kernels can be used, generally at a decreased image quality. Kernels of different design and length can be combined.

We propose an algorithm to correct for the cupping artifact inherent in CT images due to the polychromatic nature of the spectrum. This method is empirical and does not require knowledge of the spectrum and of the attenuation coefficients. The method aims at linearizing the attenuation data using a precorrection function of polynomial form. The coefficients of the polynomial are determined from a fit of some linear combined reconstructed images of the polychromatic data with a defined template. This template is obtained from the reconstruction of the polychromatic raw data and does not make any assumptions on the phantom size or of its positioning. It is shown that the fit can be performed easily solving only a linear system, making the method very fast. An example of application is given as the water precorrection. For this particular case, practical considerations are given on the definition of the template when an attenuating object table of unknown density is within the images. The method can generally correct for any kind of cupping such as scatter as well.

In the long object problem it is intended to reconstruct exactly a region-of-interest (ROI) of an object from spiral cone-beam data which covers the ROI and its immediate vicinity. One possible solution is the previously published local ROI technique. The Radon derivative data are computed for different local ROI's which are adapted to the scan path such that the contributing cone-beams are not contaminated by object information outside the local ROI. The common intersection of all local ROI's is reconstructed. The method was implemented in the filtered backprojection based 4-step algorithm. It mainly consists of explicit calculations of line integrals and their backprojection on the detector. Inside the ROI the same good image quality is achieved as in the reference case where the complete object is sampled. However, the 4-step algorithm suffers from a long computation time. It is found that the demanding filtering operations are equivalent to a number of spatially variant 1D Hilbert transforms. Thus filtering can be performed by 1D convolutions. To optimize the convolution kernels with respect to numerical stability, the empirical point spread function corresponding to the filtering of the 4-step algorithm is analyzed. Modifications of the theoretical filter kernels are derived and discussed.

The response of a point object in a cone beam (CB) spiral scan is analysed. Based on the result, a reconstruction algorithm for long object imaging in spiral scan cone beam CT is developed. A region-of-interest (ROI) of the long object is scanned with a detector smaller than the ROI, and a portion of it can be reconstructed without contamination from overlaying materials. The top and bottom surfaces of the ROI are defined by two sets of PI lines near the two ends of the spiral path. With this novel definition of the top and bottom ROI surfaces and through the use of projective geometry, it is straightforward to partition the cone beam image into regions corresponding to projections of the ROI, the overlaying objects or both. This also simplifies computation at source positions near the spiral ends, and makes it possible to reduce radiation exposure near the spiral ends substantially through simple hardware collimation. Simulation results to validate the algorithm are presented.

Presents a spiral scan cone beam reconstruction algorithm in which image reconstruction proceeds via backprojection in the object space. In principle the algorithm can reconstruct sectional ROI in a long object. The approach is a generalization of the cone beam backprojection technique developed by Kudo and Saito in two aspects: the resource-demanding normalization step in the Kudo and Saito's (1994) algorithm is eliminated through the technique of data combination which the authors published earlier, and the elimination of the restriction that the detector be big enough to capture the entire image of the ROI. Restricting the projection data to the appropriate angular range required by data combination can be accomplished by a masking process. Because of the simplification resulting from the elimination of the normalization step, the most time-consuming operations of the algorithm can be approximated by the efficient step of line-by-line ramp filtering the cone beam image in the direction of the scan path, plus a correction image. The correction image, which can be computed exactly, is needed because data combination is not properly matched at the mask boundary when ramp filtering is involved. Empirical 2D PSF, the Shepp-Logan filter, and a modified ramp filter are developed to improve matching with the correction image which is computed with finite samplings. The use of transition region to further improve matching is introduced. The results of testing the algorithm on simulated phantoms are presented.

Recently a number of approaches solving the long object problem with spiral scan appeared in the literature. Unlike the algorithms which employ circular scans for solving the long object problem, with only spiral scan it is necessary to scan regions of the object adjacent to the ROI in order to reconstruct the ROI without contamination; the spiral path required beyond the ROI is referred to as overscan in the literature. Overscan exposes the regions in the long object adjacent to the ROI to radiation as well as incurs additional computation time In this paper we present a number of methods to reduce the undesirable overscan, with emphasis on the local ROI algorithm.

A number of filtered-backprojection type quasi-exact algorithms have been recently developed to reconstruct images in cone beam spiral scan. A key common feature in these algorithms is a masking process employed in filtering the cone beam image. The masking process is an approximation to restrict the line integrals intersecting the cone beam image to the appropriate angular range required for data combination. Errors in the approximation are caused by portions of some integration line segments which do not conform to proper data combination. In this paper the line segments which constitute the major source of errors in the masking process are identified. It is found that these line segments are localized in the detector projection space. The errors can be corrected by applying the filtering process to this group of line segments. It is also shown in the paper that the correction procedure can be simplified by using 1D Hilbert transforms. Improvements in image quality brought about by the correction procedure are demonstrated in simulation reconstructions.

Investigates the performance of exact reconstruction algorithms for spiral cone-beam computed tomography. The authors compare two different approaches of exact algorithms: the first one is the Radon algorithm with explicit calculation of Radon data and subsequent direct inversion, the second approach is a reformulation of the Radon algorithm as a three-dimensional (3-D) filtered backprojection (FBP) method. Both algorithms are able to reconstruct a region of interest (ROI) of a long object by using the local ROI technique. The goal of this study is to identify which algorithm has the better performance with respect to image quality and practicability. The properties of the algorithms are analyzed. Image quality is evaluated regarding artifacts, spatial as well as contrast resolution, and noise properties. The 3-D point spread function (PSF) is examined for violations of isotropy and spatial invariance. In-plane and axial resolutions are derived from the in-plane modulation transfer function (MTF) and the slice sensitivity profile (SSP), respectively. The results show that for the two implementations investigated in this study, the image quality is similar, with a slight advantage of the FBP case. The algorithms yield images almost free of artifacts but with a poor spatial resolution. Regarding practicability, however, the FBP approach seems to be a more convenient and more flexible method because of the sequential processing of the projections and the easy control of image characteristics.

The authors present a (spiral + circles) scan cone beam reconstruction algorithm in which image reconstruction proceeds via backprojection in the object space. In principle, the algorithm can reconstruct sectional region-of-interest (ROI) in a long object. The approach is a generalization of the cone beam backprojection technique developed by Kudo and Saito (1994) in two aspects: the resource-demanding normalization step in the Kudo and Saito's algorithm is eliminated through the technique of data combination that the authors published earlier, and the elimination of the restriction that the detector be big enough to capture the entire cone beam projection of the ROI. Restricting the projection data to the appropriate angular range required by data combination can be accomplished by a masking process. Because of the simplification resulting from the elimination of the normalization step, the most time-consuming operations of the algorithm can be approximated by the efficient step of line-by-line ramp filtering the cone beam image in the direction of the scan path, plus a correction image. The correction image, which can be computed exactly, is needed because data combination is not properly matched at the mask boundary when ramp filtering is involved. Empirical two-dimensional (2-D) point spread function (PSF) is developed to improve matching with the correction image which is computed with finite samplings. The use of transition region to further improve matching is introduced. The results of testing the algorithm on simulated phantoms are presented.