Cone Beam Filtered Backprojection Research Articles

Image artefact propagation in motion estimation and reconstruction in interventional cardiac C-arm CT

The acquisition of data for cardiac imaging using a C-arm computed tomography system requires several seconds and multiple heartbeats. Hence, incorporation of motion correction in the reconstruction step may improve the resulting image quality. Cardiac motion can be estimated by deformable three-dimensional (3D)/3D registration performed on initial 3D images of different heart phases. This motion information can be used for a motion-compensated reconstruction allowing the use of all acquired data for image reconstruction. However, the result of the registration procedure and hence the estimated deformations are influenced by the quality of the initial 3D images. In this paper, the sensitivity of the 3D/3D registration step to the image quality of the initial images is studied. Different reconstruction algorithms are evaluated for a recently proposed cardiac C-arm CT acquisition protocol. The initial 3D images are all based on retrospective electrocardiogram (ECG)-gated data. ECG-gating of data from a single C-arm rotation provides only a few projections per heart phase for image reconstruction. This view sparsity leads to prominent streak artefacts and a poor signal to noise ratio. Five different initial image reconstructions are evaluated: (1) cone beam filtered-backprojection (FDK), (2) cone beam filtered-backprojection and an additional bilateral filter (FFDK), (3) removal of the shadow of dense objects (catheter, pacing electrode, etc) before reconstruction with a cone beam filtered-backprojection (cathFDK), (4) removal of the shadow of dense objects before reconstruction with a cone beam filtered-backprojection and a bilateral filter (cathFFDK). The last method (5) is an iterative few-view reconstruction (FV), the prior image constrained compressed sensing combined with the improved total variation algorithm. All reconstructions are investigated with respect to the final motion-compensated reconstruction quality. The algorithms were tested on a mathematical phantom data set with and without a catheter and on two porcine models using qualitative and quantitative measures. The quantitative results of the phantom experiments show that if no dense object is present within the scan field of view, the quality of the FDK initial images is sufficient for motion estimation via 3D/3D registration. When a catheter or pacing electrode is present, the shadow of these objects needs to be removed before the initial image reconstruction. An additional bilateral filter shows no major improvement with respect to the final motion-compensated reconstruction quality. The results with respect to image quality of the cathFDK, cathFFDK and FV images are comparable. In conclusion, in terms of computational complexity, the algorithm of choice is the cathFDK algorithm

SU‐FF‐I‐42: Improving Noise Uniformity in Volumetric CT Via ROI‐Based Weighting Scheme in Cone Beam Image Reconstruction

Purpose: To present an ROI‐based weighting scheme for cone beam image reconstruction to improve noise uniformity. Method and Materials: In CT imaging, the noise in near‐iso area is significantly larger than outer area. The root cause of this phenomenon is that the system transfer function of backprojection is reversely proportional to the iso‐distance of pixels to be reconstructed. Though this phenomenon is intrinsic and has been observing since the advent of CT imaging, we address this undesired noise non‐uniformity by extending the 3D weighted cone beam filtered backprojection (CB‐FBP) algorithm that has been previously published by us. As demonstrated previously, the noise level of images reconstructed by the 3D weighted CB‐FBP algorithm monotonically increases with the strength of 3D weighting. In addition to its dependence on view angle, orthogonal iso‐distance and cone angle, the extended 3D weighting scheme integrates a dependence on the iso‐distance of pixels to be reconstructed, i.e., the larger the iso‐distance, the stronger the weighting. Consequently, the noise at near‐iso area is reduced while that at outer area is increased. Results: The helical body phantom (HBP) simulated by computer is employed to evaluate the performance of the extended 3D weighting scheme to improve noise uniformity, in which 128 detector rows corresponding to 8.46 degree cone angle is assumed. The results shows that, with the integration of dependence on the iso‐distance of pixels to be reconstructed, the extended weighting scheme can improve noise uniformity by more than 30%, while its efficacy in suppressing artifacts caused by longitudinal truncation can be retained. Conclusion: The intrinsic noise non‐uniformity in CT images can be improved significantly using the ROI‐based 3D weighting scheme proposed in this study. It is believed that, the extended 3D weighting scheme can find its applications in the pursuit of clinical excellence using volumetric CT as the modality.

Minimization of over-ranging in helical volumetric CT via hybrid cone beam image reconstruction-Benefits in dose efficiency

Diagnostic computed tomography (CT) images are usually acquired in both helical and axial scans in the clinical applications using cone beam volumetric CT. In addition to faster patient throughput, a helical scan in volumetric CT can provide better image quality because of the satisfaction of data sufficiency condition, and thus has been performed far more frequently so far in the clinic. However, the first and last images in a helical scan are usually prescribed at the locations that are half helical turn indented from the starting and ending points of the scan. Due to such an indention, the dose efficiency of helical scan deteriorates with increasing detector dimension along z direction. To improve the dose efficiency of helical scan in volumetric CT, a hybrid helical cone beam filtered backprojection (CB-FBP) algorithm is presented here to reconstruct helical images beyond the conventional indented image zone. The hybrid algorithm is a combination of the ray-wise three-dimensional (3D) weighted CB-FBP algorithms that are recently proposed for helical and axial CB image reconstructions. Through the hybridization, the ray-wise 3D weighting becomes dependent on both helical pitch and image slice location. Phantom study shows that the conventional indented image zone in helical scan can be extended substantially by using the hybrid algorithm. Consequently, the dose efficiency of volumetric CT in helical scan can be improved significantly. It is believed that, with increasing detector dimension along z direction in cone beam volumetric CT, the hybrid algorithm will become more attractive in clinical applications.

SU‐GG‐I‐32: Optimization of Dose Efficiency in Helical Scan and Image Reconstruction at Dynamically Variable Pitches

Purpose: To present a cone beam helical image reconstruction algorithm for CT diagnostic imaging at dynamically variable pitches and its optimization in dose efficiency. Method and Materials: The ray‐wise 3D weighted helical cone beam filtered backprojection (CB‐FBP) algorithm is extended to carry out image reconstruction at dynamically variable helical pitch, in which the filtering process is carried out in the cone‐parallel geometry along the tangential direction of the helical source trajectory. Consequently, the filtering paths are straight lines at dynamically invariable pitch, but become curves at dynamically variable helical pitches. In addition, since the pitch variation may be caused by either acceleration or deceleration, the filtering paths can be curves containing inflexions. The FORBILD head and thorax phantoms are utilized to evaluate the performance of the extended algorithm. The dynamical variation range of normalized helical pitch in the evaluation is between 0.5:1 and 1.5, which is quite large from the perspective of clinical applications. Moreover, the optimization in dose efficiency is studied by evaluating the noise characteristics at various transitions of helical pitches. Results: The phantom study shows that, at a wide variation of helical pitches, the extended ray‐wise 3D weighted helical CB‐FBP algorithm can provide a well‐balanced imaging performance over reconstruction accuracy, spatial resolution and noise characteristics, while a large field of view can be maintained. Meanwhile, the noise uniformity of the presented algorithm can be improved by optimizing the ray‐wise 3D weighting parameters with the dynamic variation of helical pitch during the scan. Conclusion: Based on the experimental evaluation, especially its robustness over a large variation range of helical pitches, it is expected that the extended ray‐wise 3D weighted CB‐FBP algorithm can meet the challenges posed by advanced clinical applications, in which helical scanning and image reconstruction at dynamically variable pitches and maintenance of noise characteristics are demanded.

Cone-beam filtered backprojection image reconstruction using a factorized weighting function

We present several new families of mathematically exact cone-beam image reconstruction algorithms for a general source trajectory that fulfills Tuy's data sufficiency condition. The basic structure of the new algorithms is to reconstruct images via filtered backprojection (FBP) with a 1-D shift-invariant filter. Specifically, the general weighting function w(x,;t) for redundant data was decomposed into three components w1(x,), w2(x,t), and sgn[·y(t)], viz. w(x,;t)=[w1(x,)w2(x,t)sgn(·y(t))]. Based upon the normalization condition of the weighting function, the first component w1(x,) may be calculated using the second component w2(x,t) Thus, the design of the weighting function was reduced to the selection of the second component w2(x,t). Using this scheme, it has been demonstrated that, for a given scanning configuration, one may develop infinitely many different, exact cone-beam FBP image reconstruction algorithms. To demonstrate how this general procedure may be used to develop FBP image reconstruction algorithms, a two-concentric-circle scanning configuration is discussed in detail. Numerical simulations have been conducted to validate several of the derived image reconstruction algorithms. Several possible scan strategies are presented, and the possibility of performing multiple reconstructions with different scan configurations to reduce image noise is described. Noise properties also have been numerically studied for the implemented image reconstruction algorithms, then compared with two other shift-invariant FBP reconstruction algorithms.

Handling data redundancy in helical cone beam reconstruction with a cone‐angle‐based window function and its asymptotic approximation

A cone-angle-based window function is defined in this manuscript for image reconstruction using helical cone beam filtered backprojection (CB-FBP) algorithms. Rather than defining the window boundaries in a two-dimensional detector acquiring projection data for computed tomographic imaging, the cone-angle-based window function deals with data redundancy by selecting rays with the smallest cone angle relative to the reconstruction plane. To be computationally efficient, an asymptotic approximation of the cone-angle-based window function is also given and analyzed in this paper. The benefit of using such an asymptotic approximation also includes the avoidance of functional discontinuities that cause artifacts in reconstructed tomographic images. The cone-angle-based window function and its asymptotic approximation provide a way, equivalent to the Tam-Danielsson-window, for helical CB-FBP reconstruction algorithms to deal with data redundancy, regardless of where the helical pitch is constant or dynamically variable during a scan. By taking the cone-parallel geometry as an example, a computer simulation study is conducted to evaluate the proposed window function and its asymptotic approximation for helical CB-FBP reconstruction algorithm to handle data redundancy. The computer simulated Forbild head and thorax phantoms are utilized in the performance evaluation, showing that the proposed cone-angle-based window function and its asymptotic approximation can deal with data redundancy very well in cone beam image reconstruction from projection data acquired along helical source trajectories. Moreover, a numerical study carried out in this paper reveals that the proposed cone-angle-based window function is actually equivalent to the Tam-Danielsson-window, and rigorous mathematical proofs are being investigated.

SU‐FF‐I‐03: Computation‐Efficient Cone Beam Image Reconstruction for Image‐ Guided Radiation Therapy Applications Using 3D Weighted Filtered Backprojection (CB‐FBP) Algorithm

Purpose: To extend the 3D weighted cone beam filtered backprojection (CB‐FBP) algorithm for diagnostic CT imaging to image‐guided radiation therapy (IGRT) applications. Method and Materials: 3D isotropic spatial resolution is one of the most attracting features of state‐of‐the‐art volumetric CT for diagnostics imaging. However, in IGRT treatment planning, the CT image slice thickness is usually larger than what is determined by detector row width (namely thin image). A straightforward way to generate thicker image is the combination of weighted adjacent thin images in image domain, which is computationally expensive because each thin image has to go through a computation expensive 3D backprojection. Another way is to carry out cross‐row filtering in projection domain, which may cause shading/glaring artifacts and uneven slice thickness as isotropic 3D geometry is distorted. To optimize both image quality (IQ) and computational efficiency, a virtual reconstruction plane (RP) based algorithm is proposed and implemented. By using the 3D weighted CB‐FBP algorithm, a thick image is still a weighted combination of adjacent thin images, but the combination is implemented in projection domain using virtual RPs. To maintain the IQ of thick image, the 3D weighted CB‐FBP algorithm is applied by tracking re‐sampled projection data. The tracking process is to improve computational efficiency further by making use of the projection data corresponding to involved virtual RPs only, while the re‐sampling process is to improve IQ by increasing the in‐plane sampling‐rate in virtual RPs. Results: By using a helical body phantom, spatial resolution phantom and 20 cm water phantom, the performance of the proposed algorithm, such as suppression of artifacts, uniformity of slice thickness and noise characteristics, are experimentally evaluated and verified. Conclusion: The experimental evaluation shows the proposed algorithm is indeed an optimized image reconstruction solution for IGRT applications in terms of both image quality and computational efficiency.

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.

A cone beam filtered backprojection (CB-FBP) reconstruction algorithm for a circle-plus-two-arc orbit.

The circle-plus-arc orbit possesses advantages over other "circle-plus" orbits for the application of x-ray cone beam (CB) volume CT in image-guided interventional procedures requiring intraoperative imaging, in which movement of the patient table is to be avoided. A CB circle-plus-two-arc orbit satisfying the data sufficiency condition and a filtered backprojection (FBP) algorithm to reconstruct longitudinally unbounded objects is presented here. In the circle suborbit, the algorithm employs Feldkamp's formula and another FBP implementation. In the arc suborbits, an FBP solution is obtained originating from Grangeat's formula, and the reconstruction computation is significantly reduced using a window function to exclude redundancy in Radon domain. The performance of the algorithm has been thoroughly evaluated through computer-simulated phantoms and preliminarily evaluated through experimental data, revealing that the algorithm can regionally reconstruct longitudinally unbounded objects exactly and efficiently, is insensitive to the variation of the angle sampling interval along the arc suborbits, and is robust over practical x-ray quantum noise. The algorithm's merits include: only 1D filtering is implemented even in a 3D reconstruction, only separable 2D interpolation is required to accomplish the CB backprojection, and the algorithm structure is appropriate for parallel computation.

Cone-beam filtered-backprojection algorithm for truncated helical data

This paper investigates 3D image reconstruction from truncated cone-beam (CB) projections acquired with a helical vertex path. First, we show that a rigorous derivation of Grangeat's formula for truncated projections leads to a small additional term compared with previously published similar formulations. This correction term is called the boundary term. Next, this result is used to develop a CB filtered-backprojection (FBP) algorithm for truncated helical projections. This new algorithm only requires the CB projections to be measured within the region that is bounded, in the detector, by the projections of the upper and lower turns of the helix. Finally, simulations with mathematical phantoms demonstrate that: (i) the boundary term is necessary to obtain high-quality imaging of low-contrast structures and (ii) good image quality is obtained even with large values of the pitch of the helix.

Quantitative analysis of image truncation in focal-beam CT

The authors measured truncation artifacts using a phantom model of the human thorax. Reconstructions were performed with both iterative cone-beam transmission maximum likelihood (TRML) and cone-beam filtered backprojection (CB-FBP). When CB-FBP was used, image truncation created 'streak' artifacts of increased density, distorted the elliptical phantom body contour into a circle with reduced radius, and increased the apparent density of the lungs. SPECT attenuation compensation using this truncated CB-FBP map produced line-source activities that were only 65% of the correct 'in-air' values. Thus, CB-FBP attenuation maps will generally be unacceptable for clinical SPECT attenuation compensation. The truncation-streak artifacts were eliminated with TRML, but in some regions the body contour was not sharply defined, and the reconstructed density was low in the lungs and nonzero outside the body contour. An elliptical support prior eliminated the 'in-air' density and improved the accuracy in the lungs, as determined by narrow-beam transmission measurements with a germanium detector. For iterations above twenty-four, TRML images were noisier than CB-FBP images with a Hann filter, and at least thirty iterations were required for accurate reconstruction. SPECT line-source attenuation compensation with a truncated TRML map was accurate to within 20%, depending upon the slice number and the source location.

Maximum likelihood reconstruction for cone beam SPECT with camera tilt

Iterative maximum-likelihood (ML) reconstruction techniques are extended to the cone-beam SPECT (single-photon-emission computed tomography) geometry with the camera head tilted relative to the axis of rotation. The resulting code is an extension of a previous cone-beam ML code for the untilted case. The details of the code development, which included the variable camera sensitivity but excluded resolution, attenuation, and scatter, are described. The code is tested as a function of iteration in comparison with an existing tilt-angle filtered-backprojection (FBP) code, which has known distortions due to an incomplete theory. For a variety of point sources, as well as for a brain phantom, the tilt-angle cone-beam ML code (TCBML) performs visually and quantitatively better than cone-beam FBP (CB-FBP), and it removes the distortions inherent in CB-FBP. The TCBML code requires substantial computation time, which depends on the source geometry being reconstructed and varies in the present work from 3.5 to 50 times longer than the CB-FBP code. >