An approximate short scan helical FDK cone beam algorithm based on nutating curved surfaces satisfying the Tuy's condition

Interesting detector shapes for third generation CT scanners

PURPOSE

To discuss options in designing detector shapes in third generation CT and to quantify potential cost savings for compact third generation CT systems, and to extend the work from two-dimensional fan-beam CT to three-dimensional cone-beam CT for circular, sequential, and spiral scan trajectories.

METHODS

Third generation CT scanners typically comprise detectors which are flat or whose shape is the segment of a cylinder or a sphere that is focused onto the focal spot of the x-ray source. There appear to be two design criteria that favor this choice of detector shape. One is the possibility of performing fan-beam and cone-beam filtered backprojection in the native geometry (without rebinning) and the other criterion could be to enable the early use of focused antiscatter grids. It is less known, however, that other detector shapes may also have these properties. While these designs have been evaluated for 2D CT from a theoretical standpoint more than one decade ago the authors revisit and generalize these considerations, extend them to 3D circular, sequential, and spiral cone-beam CT and propose an optimal design in terms of detector costs while keeping image quality constant. Their considerations and conclusions are based on considering the sampling density of the x-rays, including the effects of finite focal spot and finite detector element size. Proposing image reconstruction algorithms or numerically evaluating the results by reconstructing simulated projection data is not within the scope of this work.

RESULTS

If the detector arc is curved to be nearly concentric with the circle describing the edge of the field of measurement significantly less detector area and detector pixels are required compared to today's third generation CT systems where the detector arc is centered about the focal spot. Combined with a detector that just covers the spiral Tam window cost savings of 60% or more are possible in compact CT systems. In terms of practicability the new designs appear to be nearly as easy to realize as today's third generation systems.

CONCLUSIONS

Compact CT systems, which require the focal spot to be mounted close to the edge of the field of measurement, may significantly benefit from using detector shapes other than the typical equiangular detector that is focused onto the focal spot.

Compressed sensing based cone-beam computed tomography reconstruction with a first-order method

PURPOSE

This article considers the problem of reconstructing cone-beam computed tomography (CBCT) images from a set of undersampled and potentially noisy projection measurements.

METHODS

The authors cast the reconstruction as a compressed sensing problem based on l1 norm minimization constrained by statistically weighted least-squares of CBCT projection data. For accurate modeling, the noise characteristics of the CBCT projection data are used to determine the relative importance of each projection measurement. To solve the compressed sensing problem, the authors employ a method minimizing total-variation norm, satisfying a prespecified level of measurement consistency using a first-order method developed by Nesterov.

RESULTS

The method converges fast to the optimal solution without excessive memory requirement, thanks to the method of iterative forward and back-projections. The performance of the proposed algorithm is demonstrated through a series of digital and experimental phantom studies. It is found a that high quality CBCT image can be reconstructed from undersampled and potentially noisy projection data by using the proposed method. Both sparse sampling and decreasing x-ray tube current (i.e., noisy projection data) lead to the reduction of radiation dose in CBCT imaging.

CONCLUSIONS

It is demonstrated that compressed sensing outperforms the traditional algorithm when dealing with sparse, and potentially noisy, CBCT projection views.

Cone-beam imaging in dentistry

Cone-beam imaging has gained broad acceptance in dentistry in the last 5 years. The purpose of this review is to describe the use in dentistry and consider issues requiring further development. Cone-beam machines emit an x-ray beam shaped liked a cone rather than a fan as in conventional computed tomography (CT) machines. After this beam passes through the patient the remnant beam is captured on an amorphous silicon flat panel or image intensifier/charge-coupled device (CCD) detector. The beam diameter ranges from 4 to 30 cm and exposes the head in one pass around the patient capturing from 160 to 599 basis images. These images are used to compute a volume from which planar or curved reconstructions can be extracted in any orientation. Voxels are isotropic and can be as small as 0.125 mm. 3-D images of bone or soft tissue surfaces can also be generated. In dentistry the most common indications for cone-beam imaging are assessment of the jaws for placement of dental implants, evaluation of the temporomandibular joints for osseous degenerative changes, examination of teeth and facial structures for orthodontic treatment planning, evaluation of the proximity of lower wisdom teeth to the mandibular nerve prior to extraction, and evaluation of teeth and bone for signs of infections, cysts, or tumors. Cone-beam images have largely replaced conventional tomography for these tasks. The effective dose from cone-beam imaging ranges from 6 to 477 microSv. The cost of the equipment is relatively low, about $150,000 to $300,000. Issues to be considered are the training of individuals making and interpreting cone-beam images, as well as means to further reduce patient exposure.

A three-dimensional-weighted cone beam filtered backprojection (CB-FBP) algorithm for image reconstruction in volumetric CT—helical scanning

Based on the structure of the original helical FDK algorithm, a three-dimensional (3D)-weighted cone beam filtered backprojection (CB-FBP) algorithm is proposed for image reconstruction in volumetric CT under helical source trajectory. In addition to its dependence on view and fan angles, the 3D weighting utilizes the cone angle dependency of a ray to improve reconstruction accuracy. The 3D weighting is ray-dependent and the underlying mechanism is to give a favourable weight to the ray with the smaller cone angle out of a pair of conjugate rays but an unfavourable weight to the ray with the larger cone angle out of the conjugate ray pair. The proposed 3D-weighted helical CB-FBP reconstruction algorithm is implemented in the cone-parallel geometry that can improve noise uniformity and image generation speed significantly. Under the cone-parallel geometry, the filtering is naturally carried out along the tangential direction of the helical source trajectory. By exploring the 3D weighting's dependence on cone angle, the proposed helical 3D-weighted CB-FBP reconstruction algorithm can provide significantly improved reconstruction accuracy at moderate cone angle and high helical pitches. The 3D-weighted CB-FBP algorithm is experimentally evaluated by computer-simulated phantoms and phantoms scanned by a diagnostic volumetric CT system with a detector dimension of 64 x 0.625 mm over various helical pitches. The computer simulation study shows that the 3D weighting enables the proposed algorithm to reach reconstruction accuracy comparable to that of exact CB reconstruction algorithms, such as the Katsevich algorithm, under a moderate cone angle (4 degrees) and various helical pitches. Meanwhile, the experimental evaluation using the phantoms scanned by a volumetric CT system shows that the spatial resolution along the z-direction and noise characteristics of the proposed 3D-weighted helical CB-FBP reconstruction algorithm are maintained very well in comparison to the FDK-type algorithms. Moreover, the experimental evaluation by clinical data verifies that the proposed 3D-weighted CB-FBP algorithm for image reconstruction in volumetric CT under helical source trajectory meets the challenges posed by diagnostic applications of volumetric CT imaging.

Tilted plane Feldkamp type reconstruction algorithm for spiral cone beam CT

An approximate image reconstruction method for spiral cone beam computed tomography (CT), called tilted plane Feldkamp type reconstruction algorithm (TPFR), is presented in this paper, which extends Feldkamp cone beam reconstruction algorithm to deal with its inaccuracy and artifact problems caused by large cone angle. This is done by tilting the reconstructing planes to minimize the cone angle and optimally fit the spiral segment of the source. The tilted plane image reconstruction requires reforming the three-dimensional projection data set for the tilted plane and application of Feldkamp algorithm to the reformed data set. Analytical and computational results can show that the image reconstruction performance of the proposed TPFR algorithm is superior to that of the Feldkamp reconstruction algorithm in the image quality, volume coverage speed, maximum achievable pitch value, and slice sensitivity profiles. Moreover, it provides more accurate image reconstruction than the existing two-dimensional reconstruction algorithms.