Kwok Tam

Exact cone beam CT with a spiral scan.

A method is developed which makes it possible to scan and reconstruct an object with cone beam x-rays in a spiral scan path with area detectors much shorter than the length of the object. The method is mathematically exact. If only a region of interest of the object is to be imaged, a top circle scan at the top level of the region of interest and a bottom circle scan at the bottom level of the region of interest are added. The height of the detector is required to cover only the distance between adjacent turns in the spiral projected at the detector. To reconstruct the object, the Radon transform for each plane intersecting the object is computed from the totality of the cone beam data. This is achieved by suitably combining the cone beam data taken at different source positions on the scan path; the angular range of the cone beam data required at each source position can be determined easily with a mask which is the spiral scan path projected on the detector from the current source position. The spiral scan algorithm has been successfully validated with simulated cone beam data.

Filtering point spread function in backprojection cone-beam CT and its applications in long object imaging

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.

Exact (spiral+circles) scan region-of-interest cone beam reconstruction via backprojection

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 Saitos 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.

Region-of-interest imaging in cone beam computerized tomography

Imaging a sectional region within an object with a detector just big enough to cover the sectional region-of-interest is analyzed. We show that with some suitable choice of scanning configuration and with an innovative method of data combination, all the Radon data can be obtained accurately. The algorithm is mathematically exact, and requires no iterations and no additional measurements. The method can be applied to inspect portions of large industrial objects in industrial imaging, as well as to image portions of human bodies in medical diagnosis.

Optimization of derivative kernels for exact cone-beam ROI reconstruction in spiral computed tomography

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.

Eliminating the second-intersection contributions to spiral scan cone beam CT

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.

Exact spiral scan region-of-interest cone beam CT via backprojection

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 Saitos (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.

Improving large angle cone beam CT image reconstruction with practical supplementary information

Single circle cone beam scan is simple and fast to execute and image reconstruction with the Feldkamp algorithm is efficient, thus it is widely employed in a number of major medical imaging modalities. Cone beam scanners employing large area flat panel detectors with 256 rows or more are expected to appear on the market in the next few years. The large number of rows allows the collection of a large quantity of data in a very short time, and thus the new generation of scanners will be suited for scanning dynamic objects. Because of its speed single circle scan will be ideal for such scans. In 3D angio systems employing C arms the popular scan mode is circular arc, which is less complete compared to single circle scan. It is well known that a single circle scan path with Feldkamp reconstruction does not yield complete information to reconstruct the object. There are missing Radon data located along the rotation axis and its neighborhood In this paper we investigate the improvement to lite single circle scan reconstruction images with the use of supplemental), information. In particular we study a supplementary line scan and a supplementary circle scan. We also discuss the use of other sources of supplementary information, including topogram and a priori information.

Overscan reduction in spiral scan long object problem

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.