Cone-beam Filtered Backprojection Algorithm Research Articles

Optimization of slice sensitivity profile for radiographic tomosynthesis

Similar to other tomographic imaging modalities, the slice sensitivity profile (SSP) is an important image quality metric for radiographic tomosynthesis. In this study, the relationship between the acquisition angular range (Theta) and the SSP for the linear trajectory system was carefully investigated from both theoretical and experimental perspectives. A mathematical SSP model was derived for arbitrary points in the reconstructed volume. We used a newly developed flat-panel tomosynthesis prototype system to experimentally validate the mathematical model from 20 degrees (+/-10 degrees) to 60 degrees (+/-30 degrees) angular ranges. The SSP was measured by imaging an edge phantom placed at an angle with respect to the detector plane using the modulation transfer function degradation (MTF-d) method. In addition to the experiments, computer simulations were performed to investigate the relationship in a wider angular range (2.5 degrees to 60 degrees). Furthermore, image data from an anthropomorphic phantom were collected to corroborate the system analysis. All the images in this study were constructed using a 3D view-weighted cone-beam filtered backprojection algorithm (3D VW CB-FBP). The theoretical analysis reveals that the SSP of linear trajectory tomosynthesis is inversely proportional to tan(Theta/2). This theory was supported by both simulation (chi2=1.415, DF=7, p =0.985) and phantom experiment (r=0.999, p < 0.001) and was further confirmed by an analysis of the reconstructed images of an anthropomorphic phantom. The results imply that the benefit of narrower SSP by increasing angular range quickly diminishes once beyond 40 degrees. The advantages of the MTF-d method were also demonstrated.

Composite cone-beam filtered backprojection algorithm based on nutating line

The FDK algorithm is the most popular cone beam algorithm in the medical and industrial imaging field. Due to data insufficiency acquired from a circular trajectory, the images reconstructed by the FDK algorithm suffer from the intensity droping with increasing cone angle. To overcome the drawback, a modified FDK algorithm is presented by convert the 1D ramp filtering direction from along the horizontal lines to along the nutating lines based on the result of Turbell. Unlike Turbell's method, there is no need for our algorithm to rebin the cone-beam data into 3D parallel-beam data before reconstructing. Moreover pre-weighting of the projection data is corrected by compensating for the cone angle effect. In addition, another correction term derived from the result of Hu is also induced into our algorithm. The simulation experiments demonstrate that the final algorithm can suppress the intensity drop associated with the FDK algorithm.

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 × 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°) 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.

Extending Three-Dimensional Weighted Cone Beam Filtered Backprojection (CB-FBP) Algorithm for Image Reconstruction in Volumetric CT at Low Helical Pitches

A three-dimensional (3D) weighted helical cone beam filtered backprojection (CB-FBP) algorithm (namely, original 3D weighted helical CB-FBP algorithm) has already been proposed to reconstruct images from the projection data acquired along a helical trajectory in angular ranges up to [0, 2 π]. However, an overscan is usually employed in the clinic to reconstruct tomographic images with superior noise characteristics at the most challenging anatomic structures, such as head and spine, extremity imaging, and CT angiography as well. To obtain the most achievable noise characteristics or dose efficiency in a helical overscan, we extended the 3D weighted helical CB-FBP algorithm to handle helical pitches that are smaller than 1: 1 (namely extended 3D weighted helical CB-FBP algorithm). By decomposing a helical over scan with an angular range of [0, 2π + Δβ] into a union of full scans corresponding to an angular range of [0, 2π], the extended 3D weighted function is a summation of all 3D weighting functions corresponding to each full scan. An experimental evaluation shows that the extended 3D weighted helical CB-FBP algorithm can improve noise characteristics or dose efficiency of the 3D weighted helical CB-FBP algorithm at a helical pitch smaller than 1: 1, while its reconstruction accuracy and computational efficiency are maintained. It is believed that, such an efficient CB reconstruction algorithm that can provide superior noise characteristics or dose efficiency at low helical pitches may find its extensive applications in CT medical imaging.

A three-dimensional weighted cone beam filtered backprojection (CB-FBP) algorithm for image reconstruction in volumetric CT under a circular source trajectory

The original FDK algorithm proposed for cone beam (CB) image reconstruction under a circular source trajectory has been extensively employed in medical and industrial imaging applications. With increasing cone angle, CB artefacts in images reconstructed by the original FDK algorithm deteriorate, since the circular trajectory does not satisfy the so-called data sufficiency condition (DSC). A few ‘circular plus’ trajectories have been proposed in the past to help the original FDK algorithm to reduce CB artefacts by meeting the DSC. However, the circular trajectory has distinct advantages over other scanning trajectories in practical CT imaging, such as head imaging, breast imaging, cardiac, vascular and perfusion applications. In addition to looking into the DSC, another insight into the CB artefacts existing in the original FDK algorithm is the inconsistency between conjugate rays that are 180° apart in view angle (namely conjugate ray inconsistency). The conjugate ray inconsistency is pixel dependent, varying dramatically over pixels within the image plane to be reconstructed. However, the original FDK algorithm treats all conjugate rays equally, resulting in CB artefacts that can be avoided if appropriate weighting strategies are exercised. Along with an experimental evaluation and verification, a three-dimensional (3D) weighted axial cone beam filtered backprojection (CB-FBP) algorithm is proposed in this paper for image reconstruction in volumetric CT under a circular source trajectory. Without extra trajectories supplemental to the circular trajectory, the proposed algorithm applies 3D weighting on projection data before 3D backprojection to reduce conjugate ray inconsistency by suppressing the contribution from one of the conjugate rays with a larger cone angle. Furthermore, the 3D weighting is dependent on the distance between the reconstruction plane and the central plane determined by the circular trajectory. The proposed 3D weighted axial CB-FBP algorithm can be implemented in either the native CB geometry or the so-called cone-parallel geometry. By taking the cone-parallel geometry as an example, the experimental evaluation shows that, up to a moderate cone angle corresponding to a detector dimension of 64 × 0.625 mm, the CB artefacts can be substantially suppressed by the proposed algorithm, while advantages of the original FDK algorithm, such as the filtered backprojection algorithm structure, 1D ramp filtering and data manipulation efficiency, are maintained.

Performance of quasi-exact cone-beam filtered backprojection algorithm for axially truncated helical data

Concerns the problem of tomographic reconstruction from axially truncated cone-beam projections acquired with a helical vertex path. Very recently, Kudo et al. (J. Opt. Soc. Am. A, vol. 1, p. 612-19, 1984) developed a quasi-exact filtered backprojection algorithm for this problem. The purpose of this paper is to evaluate the performances of the quasi-exact algorithm by comparing it with variants of the approximate Feldkamp algorithm. The results show that the quasi-exact algorithm possesses the following two advantages over the Feldkamp algorithm. The first advantage is the improved image quality when the pitch of the helix is large. The second advantage is the use of a detector area close to the minimum detector area compatible with exact reconstruction. This area is shown to be much smaller than that required by the Feldkamp algorithm for typical geometries. One disadvantage of the quasi-exact algorithm is the computational time which is much longer than for the Feldkamp algorithm.

3-D image reconstruction with veiling glare correction to improve the contrast of 3-D reconstructed vascular images

The authors are developing an imaging system for three-dimensional (3-D) image analysis of vascular images. The purpose is to enhance the performance of clinicians in assessing anatomical information such as the orientation of blood vessels, cross-sectional area, surface shape and volume of vascular disease. The prototype system takes measurements in a short period of time by an X-ray rotational angiographic system using a CT gantry equipped with a cone-beam X-ray source and an image intensifier. The 3-D image reconstruction from two-dimensional (2-D) projections is performed by a short scan cone-beam filtered backprojection algorithm. The preprocessing of the 3-D image reconstruction includes the correction of the geometrical distortions and the shading artifact introduced by the image intensifier. Here, the authors present the short scan cone-beam filtered backprojection with scatter and veiling glare correction to improve the contrast sensitivity of 3-D reconstructed images. From results of the application to a patient's abdominal blood vessels, the authors show the effectiveness of these methods.

Cone beam SPECT reconstruction with camera tilt

The authors modified the cone beam filtered backprojection algorithm of L.A. Feldkamp et al. (1984) and applied it to the symmetric tilt-angle case. Both the modifications of the algorithm and a single preliminary test are reported.