Zikuan Chen

Three-dimensional point spread function measurement of cone-beam computed tomography system by iterative edge-blurring algorithm

With separability assumed, we decompose a three-dimensional point spread function (3D PSF) into two-dimensional (2D) PSFs and further into one-dimensional (ID) PSFs. Based on the observation of the location invariance of a step edge under convolution, we propose a rectification procedure to automatically establish the step-edge function from a blurred edge profile. The ID PSF is modelled as a single-parameter Gaussian function, which is determined by iteratively blurring a step-edge function into a spread edge profile. A plastic solid ball (diameter approximately 6 mm) is used to provide double-edged rectangular functions along scanlines passing through the ball centre, and correspondingly, the reconstructed digital volume provides the blurred rectangular profiles. Experimenting with a cone-beam computed tomography system, we demonstrate the iterative edge-blurring algorithm for PSF measurement. By repositioning the ball phantom in the object support space, we measure the systems spatial variance in terms of full-width-at-half-maximum (FWHM) of the local PSFs. Specifically, we obtained the FWHMs for three specific locations at (0, 0, -40 mm), (0, 0, 0) and (0, 0, 40 mm), which are given by 0.92 +/- 0.10 mm, 0.65 +/- 0.08 mm and 0.93 +/- 0.10 mm, respectively.

Why should breast tumour detection go three dimensional

Although x-ray mammography is widely developed for breast tumour detection, it suffers from spatial superposition in its two-dimensional (2D) representation of a three-dimensional (3D) breast structure. Accordingly, 3D breast imaging, such as cone-beam computed tomography (CT), arises at the historic moment. In this paper, we theoretically elucidate the spatial superposition effect associated with x-ray mammography on breast tumour detection. This explanation is based on the line integral of x-ray traversing a composite breast model. As a result, we can characterize the difficulty of detecting small tumours in terms of local intensity contrast in x-ray images. In comparison, we also introduce cone-beam CT breast imaging for 3D breast volume representation, which offers advantages for breast mass segmentation and measurement. The discussion is demonstrated with an experiment with a breast surgical specimen. In conclusion, we strongly believe that 3D volumetric representation allows for more accurate breast tumour detection.

Preliminary system characterization of flat-panel-detector-based cone-beam CT for breast imaging

Conventional film-screen mammography is the most effective tool for the early detection of breast cancer currently available. However, conventional mammography has relatively low sensitivity to detect small breast cancers (under several millimeters) owing to an overlap in the appearances of benign and malignant lesions, and surrounding structure. The limitations accompanying conventional mammography is to be addressed by incorporating a cone beam CT imaging technique with a recently developed flat panel detector. Computer simulation and preliminary studies have been performed to prove the feasibility of developing a flat panel detector-based cone beam CT breast imaging (FPD-CBCTBI) technique. A preliminary system characterization study of flat panel detector-based cone beam CT for breast imaging was performed to confirm the findings in the computer simulation and previous phantom studies using the current prototype cone beam CT scanner. The results indicate that the CBCTBI technique effectively removes structure overlap and significantly improves the detectability of small breast tumors. More importantly, the results also demonstrate CBCTBI offers good image quality with the radiation dose level less than or equal to that of conventional mammography. The results from this study suggest that FPD-CBCTBI is a potentially powerful breast-imaging tool.

Filling the Radon domain in computed tomography by local convex combination

Radon data interpolation is a necessary procedure in computed tomography (CT), especially for reconstruction from divergent beam scanning. In a polar-grid representation, the Radon data of a fanbeam projection are populated on an arc, rather on a radial line. Collectively, the Radon data generated from a fanbeam CT system are unevenly populated: The population becomes sparser as the polar distance increases. In CT reconstruction, the Fourier central slice theorem requires a radial scanline full of Radon data. Therefore the vacant entries of a scanline must be filled by interpolation. In addition, interpolation is also required in polar-to-Cartesian conversion. In this paper we propose a practical interpolation technique for filling the vacant entries by local convex combination. It is a linear interpolant that generates a value for a grid point from the available data lying in its neighborhood, by a weighted average, with the weights corresponding to the inverse distances. In fact, the linear convex combination serves as a general flat-smoothing operation in filling a vacancy. Specifically, this technique realizes a variety of linear interpolations, including nearest-neighbor replication, two-point collinear, three-point triangulation, and four-point quadrilateral, and local extrapolation, in a unified framework. Algorithms and a simulation demonstration are provided.

Blood flow measurement by cone-beam CT bolus imaging

Via angiographic injection, blood vessels become visible in X-ray imaging. Based on dynamic bolus tracking and static vessel volume depiction, this paper presents a three-dimensional (3D) imaging method for blood flow measurement. After angiographic injection, the bolus motion in vessels in a scan field of view can be described by wash-in, equilibrium, and wash-out phases in the order of time. The cone-beam scanning produces a sequence of projection images, of which the wash-in images are used for bolus tracking, and the equilibrium images for vessel volume reconstruction. From a vessel volume, not only can we depict the vessel diameter by digital anatomical analysis, but also extract vessel centerlines by volumetric vessel segmentation and 3D skeletonization. We assume that bolus travels along the vessel centerlines, and the 3D bolus passageways can be time ticked by consulting the bolus motion in a sequence of wash-in projection images. By splitting this sequence into two subsequences (different by a delay of a few frames) and considering them as two sequences of two-view image pairs, we can calculate a 3D bolus passageway by two-view stereo reconstruction and then correct the excursions by a nudge algorithm (3D bolus point adjustment in reference to 3D vessel skeleton). Alternatively, by cone-beam reprojecting the 3D skeleton and consulting the 2D bolus motion manifested in wash-in projection images, we can tick off the 3D skeleton by time and thereby calculating bolus pathlength and flow velocity. Numerical simulations and phantom experiments are reported.

Supergridded cone-beam reconstruction and its application to point-spread function calculation

In cone-beam computed tomography (CBCT), the volumetric reconstruction may in principle assume an arbitrarily fine grid. The supergridded cone-beam reconstruction refers to reconstructing the object domain or a subvolume thereof with a grid that is finer than the proper computed tomography sampling grid (as determined by gantry geometry and detector discreteness). This technique can naturally reduce the voxelization effect, thereby retaining more details for object reproduction. The grid refinement is usually limited to two or three refinement levels because the detail pursuit is eventually limited by the detector discreteness. The volume reconstruction is usually targeted to a local volume of interest due to the cubic growth in a three-dimensional (3D) array size. As an application, we used this technique for 3D point-spread function (PSF) measurement of a CBCT system by reconstructing edge spread profiles in a refined grid. Through an experiment with a Teflon ball on a CBCT system, we demonstrated the supergridded volume reconstruction (based on a Feldcamp algorithm) and the CBCT PSF measurement (based on an edge-blurring technique). In comparison with a postreconstruction image refinement technique (upsampling and interpolation), the supergridded reconstruction could produce better PSFs (in terms of a smaller FWHM and PSF fitting error).

Pitfalls in point-spread-function measurement of computed tomographic system by microphantom reconstruction

Intuitively, the point spread function (PSF) of a computed tomographic (CT) system can be determined by the reconstruction of a microphantom (diam 1 mm). In conclusion, the CT PSF can be efficiently determined by an edge-based technique, such as the iterative edge-blurring algorithm.

Volume fusion for two-circular-orbit cone-beam tomography

By using the Feldkamp-Davis-Kress (FDK) algorithm, we can efficiently produce a digital volume, called the FDK volume, from cone-beam data acquired along a circular scan orbit. Due to the insufficiency of the cone-beam data set, the FDK volume suffers from nonuniform reproduction exactness. Specifically, the midplane (on the scan-orbit plane) can be exactly reproduced, and the reproduction exactness of off-midplanes decreases as the distance from the midplane increases. We describe the longitudinal falling-off degradation by a hatlike function and the spatial distribution over the object domain by an exactness volume. With two orthogonal circular scan orbits, we can reconstruct two FDK volumes and generate two exactness volumes. We propose a volume fusion scheme to combine the two FDK volumes into a single volume. Let Va and Vb denote the two FDK volumes, let Ea and Eb denote the exactness volumes for orbits Gamma(a) and Gamma(b), respectively, then the volume fusion is defined by Vab=VaWa+VbWb, with Wa=Ea/(Ea+Eb) and Wb=1-Wa. In the result, the overall reproduction exactness of Vab is expected to outperform that of Va, or Vb, or (Va+Vb)/2. In principle, this volume-fusion scheme is applicable for general cone-beam tomography with multiple nonorthogonal and noncircular orbits.

Pixel-pyramid model for divergent projection geometry

Divergent projection refers to fan-beam or cone-beam projection originating from a point source, which is commonly seen in x-ray imaging. Conventionally, the divergent projection calculation is carried out using a ray model, in which each detector pixel (cell) receives radiations emanating from a point source, in a form of straight-line ray. The finite dimension of the detector pixel develops a zero-width ray into a nonzero-width strip, with its cross section assuming the effective aperture of a detector pixel facet. In the pursuit of accuracy, we portray the divergent projection from the point source radiation on a detector cell by a pyramidal element (pyrel), which is formed by a pyramidal base (detector pixel facet) and an apex (point source). A pyrel intersects the object and circumscribes a trapezoidal zone for fan-beam projection (a frustum volume for cone-beam projection), wherein the object voxels are accumulated (appropriately weighted) to produce the detector cells signal. In addition to the forward divergent projection calculation, the pyrel model can be used for iterative object reconstruction by repeating the backprojection and reprojection. Since the pyrel model portrays more naturally the divergent projection geometry, it maximizes the calculation accuracy, though at the cost of more computations. This model may be rewarding in certain situations: (1) when the detector resolution is unacceptably low, (2) when the projection data set is severely incomplete (for example, the number of projections 40 deg). Simulations on an iterative fan-beam tomographic reconstruction, using the pyrel model, the ray model, and the voxel-splatting model, are demonstrated.

Three-dimensional PSF characterization of circle-plus-arc cone-beam computed tomography

Cone-beam CT (CBCT) realizes true three-dimensional (3D) imaging in terms of its direct volume reconstruction with isotropic resolution. However, the 3D imaging performance of a CBCT system is spatially variant (or non-uniform) over the support domain, which can be quantitatively characterized by 3D point spread function (PSF). The CBCT system PSF can be experimentally measured through the use of telfon ball and edge-spread technique. For a single circular scan orbit, its volume reconstruction fails to meet data sufficiency condition, consequently causing spatial shift variance. In the pursuit of meeting data sufficiency condition, we have proposed a circle-plus-arc CB scan scheme. The overall CBCT imaging process involves several factors, including x-ray source, cone-beam projection, and computational reconstruction; each factor can in principle be characterized by a convolution kernel or PSF. In this paper, we concentrate on the PSF characterization of circle-plus-arc algorithm. Based on the linearity of Radon transform and inverse Radon transform, we can partition the Radon domain. In particular, the circle-plus-arc scan scheme partitions the Radon domain into a donut-like region (associated with the circle scan) and funnel-like null region (provided by the arc scan). A modified FDK algorithm is responsible for donut region reconstruction, and a filtered-backprojection-styled inverse Radon transform is for the null region reconstruction. By adding them up, we obtain the complete volume reconstruction. Through the use of a bead array phantom (a 5×5×5 array), subject to cone-beam scan under different scan patterns and volume reconstruction, we calculated the local PSF blurs and the spatial variance. The result shows that, for our CBCT simulation with 28 degree cone angle, the circle scan produces a spatial variance of 9.3% and the circle-plus-arc scan reduces that to 1.8%.