Tomographic reconstruction from experimentally obtained cone-beam projections

Evaluation of tilted cone-beam CT orbits in the development of a dedicated hybrid mammotomograph

A compact dedicated 3D breast SPECT-CT (mammotomography) system is currently under development. In its initial prototype, the cone-beam CT sub-system is restricted to a fixed-tilt circular rotation around the patient's pendant breast. This study evaluated stationary-tilt angles for the CT sub-system that will enable maximal volumetric sampling and viewing of the breast and chest wall. Images of geometric/anthropomorphic phantoms were acquired using various fixed-tilt circular and 3D sinusoidal trajectories. The iteratively reconstructed images showed more distortion and attenuation coefficient inaccuracy from tilted cone-beam orbits than from the complex trajectory. Additionally, line profiles illustrated cupping artifacts in planes distal to the central plane of the tilted cone-beam, otherwise not apparent for images acquired with complex trajectories. This indicates that undersampled cone-beam data may be an additional cause of cupping artifacts. High-frequency objects could be distinguished for all trajectories, but their shapes and locations were corrupted by out-of-plane frequency information. Although more acrylic balls were visualized with a fixed-tilt and nearly flat cone-beam at the posterior of the breast, 3D complex trajectories have less distortion and more complete sampling throughout the reconstruction volume. While complex trajectories would ideally be preferred, negatively fixed-tilt source-detector configuration demonstrates minimally distorted patient images.

Cone-beam reconstruction by backprojection and filtering

A new analytical method for tomographic image reconstruction from cone-beam projections acquired on the source orbits lying on a cylinder is presented. By application of a weighted cone-beam backprojection, the reconstruction problem is reduced to an image-restoration problem characterized by a shift-variant point-spread function that is given analytically. Assuming that the source is relatively far from the imaged object, a formula for an approximate shift-invariant inverse filter is derived; the filter is presented in the Fourier domain. Results of numerical experiments with circular and helical orbits are considered.

The measurement of proton stopping power using proton-cone-beam computed tomography

A cone-beam computed tomography (CT) system utilizing a proton beam has been developed and tested. The cone beam is produced by scattering a 160 MeV proton beam with a modifier that results in a signal in the detector system, which decreases monotonically with depth in the medium. The detector system consists of a Gd2O2S:Tb intensifying screen viewed by a cooled CCD camera. The Feldkamp-Davis-Kress cone-beam reconstruction algorithm is applied to the projection data to obtain the CT voxel data representing proton stopping power. The system described is capable of reconstructing data over a 16 x 16 x 16 cm3 volume into 512 x 512 x 512 voxels. A spatial and contrast resolution phantom was scanned to determine the performance of the system. Spatial resolution is significantly degraded by multiple Coulomb scattering effects. Comparison of the reconstructed proton CT values with x-ray CT derived proton stopping powers shows that there may be some advantage to obtaining stopping powers directly with proton CT. The system described suggests a possible practical method of obtaining this measurement in vivo.

Three-dimensional computed tomographic reconstruction using a C-arm mounted XRII: image-based correction of gantry motion nonidealities

The image quality of 3D reconstructions produced using a C-arm mounted XRII depends on precise determination of the geometric parameters that describe the detector system in the laboratory frame of reference. We have designed a simplified calibration system that depends on images of a metal sphere, acquired during rotation of the gantry through 200 degrees. Angle-dependent shift corrections are obtained, accounting for nonideal motion in two directions: perpendicular to the axis of rotation and tangential to the circular trajectory (tau), and parallel to the axis of rotation (xi). Projection images are corrected prior to reconstruction using a simple shift-interpolation algorithm. We show that the motion of the gantry is highly reproducible during acquisitions within one day (mean standard deviation in tau and xi is 0.11 mm and 0.08 mm, respectively), and over 21 months (mean standard deviation in tau and xi is 0.10 mm and 0.06 mm, respectively). Reconstruction of a small-bead phantom demonstrates uniformity of the correction algorithm over the full volume of the reconstruction [standard deviation of full-width-half-maximum of the beads is approximately 0.25 pixels (0.13 mm) over the volume of reconstruction]. Our approach provides a simple correction technique that can be applied when trajectory deviations are significant relative to the pixel size of the detector but small relative to the detector field of view, and when the fan angle of the acquisition geometry is small (<20 degrees). A comparison with other calibration techniques in the literature is provided.

Cone-beam X-ray microtomography of small specimens

Microtomography is a technique for creating three-dimensional images of the internal structure of objects with high spatial resolution. This can potentially allow inspection of the architecture of breast lumpectomy specimens and visualization of tumours in small animals and also has an application as a tool for non-destructive testing. An efficient method to perform microtomography is to use an area detector and cone-beam reconstruction techniques. In this paper we report on the development of an instrument for microtomography and show example images. The equipment consists of a microfocal x-ray tube (energies and currents up to 30 kVp, 0.2 mA, focal spot size < 5 microm), a rotating specimen stage and a high-resolution x-ray image intensifier optically coupled to a CCD video camera. Data acquisition and 3D image reconstruction are performed by a desktop computer. The well-known Feldkamp cone-beam reconstruction algorithm is used to produce tomographic images from the recorded x-ray projections. The instrument can image samples with diameters of 5-50 mm and create tomographic images with spatial resolution of the order 10-100 microm and signal-to-noise ratio of better than 5:1. This work is a continuation and improvement of an earlier instrument with a low-energy x-ray source and detector.

A cone-beam megavoltage CT scanner for treatment verification in conformal radiotherapy

PURPOSE

A prototype scanner for large-volume megavoltage computed tomography (MVCT) in a clinical set-up is described. The ultimate aim is to improve treatment accuracy in conformal radiotherapy through patient set-up error reduction and transit dosimetry.

MATERIALS AND METHODS

The scanner consists of a custom-built 2D CsI(Tl) crystal array viewed by a lens and a CCD camera. Image acquisition is synchronized with radiation pulses. The 2D projections resulting from a single continuous 360 degrees gantry rotation are reconstructed using a cone-beam tomography algorithm. Prior to reconstruction, the raw projections are calibrated and corrected for centre of rotation movement and accelerator output fluctuation. The performance of the system has been evaluated by reconstructing projections of open fields, test objects and a humanoid phantom.

RESULTS

Hundreds of 2D projections can be acquired with a clinically-acceptable data collection time (about 2 min) and dose (approximately 40 cGy, with a possible four-fold reduction). A maximum density resolution of about 2% is achieved offering some soft tissue discrimination without using image enhancement tools. A spatial resolution of 2.5 mm is obtained. The reconstructed image intensity is linear with electron density over the range of interest. Coronal or sagittal slices through the 3D reconstruction of the humanoid phantom show a better delineation of structures than the corresponding portal images taken at the same orientation.

CONCLUSIONS

A similar image quality to our current single-slice MVCT scanner is achieved with the advantage of providing tens of tomographic slices for a single gantry rotation. This work demonstrates the feasibility of clinical cone-beam MVCT and indicates how this prototype can be improved.

A feasibility study for megavoltage cone beam CT using a commercial EPID

This study used a standard commercial electronic portal imaging device (EPID) area detector attached to an isocentric linear accelerator and the Feldkamp algorithm to produce cone beam tomographic reconstructions. The EPID has a active area of 32.5 x 32.5 cm2, and can record 12-bit images using two monitor units (MU), with a resolution of 2.1 x 2.0 mm2 FWHM. Since the EPID was not large enough to record the full patient projection at about 1.5 geometric magnification, it was necessary to offset the detector to collect half-cone projections. Corrections are required to convert pixel values into units of exit dose and to realign the projections to overcome the +/- 4 mm support arm sag. With a geometric magnification of 1.5 the sensitive volume is a cylinder of radius 21 cm and length 17 cm. Unfortunately, the patient couch contains metal bed support rails that lie just outside this cylinder, and produce streak artefacts in the reconstruction. Using 90 views the system delivers a central dose of 90 cGy, and has a density resolution of 4%.

Derivation and implementation of a cone-beam reconstruction algorithm for nonplanar orbits

B.D. Smith (ibid., vol.MI-4, p.15-25, 1985; Opt. Eng., vol.29, p.524-34, 1990) and P. Grangeat (These de doctorat, 1987; Lecture Notes in Mathematics 1497, p.66-97, 1991) derived a cone-beam inversion formula that can be applied when a nonplanar orbit satisfying the completeness condition is used. Although Grangeat's inversion formula is mathematically different from Smith's one, they have similar overall structures to each other. The contribution of the present paper is two-fold. First, based on the derivation of Smith, the authors point out that Grangeat's inversion formula and Smith's one can be conveniently described using a single formula (the Smith-Grangeat inversion formula) that is in the form of space-variant filtering followed by cone-beam back projection. Furthermore, the resulting formula is reformulated for data acquisition systems with a planar detector to obtain a new reconstruction algorithm. Second, the authors make two significant modifications to the new algorithm to reduce artifacts and numerical errors encountered in direct implementation of the new algorithm. As for exactness of the new algorithm, the following fact can be stated. The algorithm based on Grangeat's intermediate function is exact for any complete orbit, whereas that based on Smith's intermediate function should be considered as an approximate inverse excepting the special case where almost every plane in 3D space meets the orbit. The validity of the new algorithm is demonstrated by simulation studies.

A cone-beam filtered backprojection reconstruction algorithm for cardiac single photon emission computed tomography

A filtered backprojection reconstruction algorithm was developed for cardiac single photon emission computed tomography with cone-beam geometry. The algorithm reconstructs cone-beam projections collected from ;short scan' acquisitions of a detector traversing a noncircular planar orbit. Since the algorithm does not correct for photon attenuation, it is designed to reconstruct data collected over an angular range of slightly more than 180 degrees with the assumption that the range of angles is oriented so as not to acquire the highly attenuated posterior projections of emissions from cardiac radiopharmaceuticals. This sampling scheme is performed to minimize the attenuation artifacts that result from reconstructing posterior projections. From computer simulations, it is found that reconstruction of attenuated projections has a greater effect upon quantitation and image quality than any potential cone-beam reconstruction artifacts resulting from insufficient sampling of cone-beam projections. With nonattenuated projection data, cone beam reconstruction errors in the heart are shown to be small (errors of at most 2%).

Three-dimensional x-ray microtomography for medical and biological applications

Three-dimensional (3D) x-ray microtomography is a technique for obtaining the 3D distribution of x-ray attenuation coefficients within small objects. To obtain microtomographic images apparatus has been developed which consists of a microfocal x-ray source, a computer-controlled stage for rotating the object, a 2D multi-wire gas proportional x-ray counter and a microcomputer to control image acquisition. Projection data were generated by rotating the object to discrete orientations around a single axis until of the order of 100 2D projection images of the object were collected. The projection images were transferred to a VAX 11/750 computer for subsequent 3D reconstruction using a convolution and back-projection algorithm in cone-beam geometry. The reconstructed data, comprising cubic voxels, may be displayed as sets of sequential transaxial, sagittal and coronal planes through the object. Alternatively, perspective displays of individual orthogonal sections may be formed with either intersecting planes or with these planes projected onto the surfaces of a box-like structure. The technique provides for the investigation of small-scale structures in biological specimens and we show some illustrative images of dead insects.

True three-dimensional cone-beam reconstruction (TTCR) algorithm

A true three-dimensional cone-beam reconstruction (TTCR) algorithm for direct volume image reconstruction from 2-D cone-beam projections is developed for the complete sphere geometry. The algorithm is derived from the parallel-beam true three-dimensional reconstruction (TTR) algorithm and is based on the modified filtered backprojection technique, which uses a set of 2-D space-invariant filters. The proposed algorithm proved to be superior in spatial resolution to the parallel-beam TTR algorithm and to offer better computational efficiency.

Comments, with reply, on ;Tomographic reconstruction from experimentally obtained cone-beam projections' by S. Webb, et al

The above paper (ibid., vol.MI-6, p.67-73, 1987) purports to propose an algorithm and implementation formulas for cone-beam reconstruction. The commenters point out that the exposition of the paper is little more than a paraphrase of their own earlier work (J. Opt. Soc. Amer. A, vol.1, no.6, p.612-19, 1984). All the benefits claimed are intrinsic to the algorithm proposed and were pointed out in the commenters paper. Webb et al. also suggest the use of a modified convolution scheme previously proposed for fan-beam reconstruction. Use of this scheme does not alter the basic premise of the commenters' work and does not entitle Webb et al. to claim to have developed a new algorithm. The authors reply that their paper presents experimental results that are based on the commenters' theoretical results, which were cited in the formers' paper.

Isotope computed tomography using cone-beam geometry: a comparison of two reconstruction algorithms

A CT scanner has been constructed specifically to determine the three-dimensional distribution of bone mineral in the medullary cavities of the radius, ulna and femur. A source of x-rays (153Gd) and a multiwire proportional counter (MWPC) are mounted at opposite ends of a diameter of an annular mounting. The limb is placed on the axis of rotation of the annulus and a series of two-dimensional transmission projections are obtained at equal angular spacings over 360 degrees. The distribution of bone mineral is reconstructed from the projections either by the method of maximum entropy (ME) or by convolution and back projection (CBP). These two methods have been evaluated by reconstructing a single slice of a phantom, representing the forearm, from projections simulated by computer. With a clinically acceptable exposure time, the mean medullary densities of the ulna and radius were determined with systematic errors of less than 3.5% (ME) and 11% (CBP), although for the latter method of reconstruction the systematic error was reduced to less than 2% by increasing the number of views. The mean medullary densities of the ulna and radius were determined with precisions better than 2.5% (ME) and 3.5% (CBP).