A new scheme for view-dependent data differentiation in fan-beam and cone-beam computed tomography

Generalized-equiangular geometry CT: Concept and shift-invariant FBP algorithms

BACKGROUND

With advanced x-ray source and detector technologies being continuously developed, non-traditional CT geometries have been widely explored. Generalized-Equiangular Geometry CT (GEGCT) architecture, in which an x-ray source might be positioned radially far away from the focus of arced detector array that is equiangularly spaced, is of importance in many novel CT systems and designs.

PURPOSE

GEGCT, unfortunately, has no theoretically exact and shift-invariant analytical image reconstruction algorithm in general. In this study, to obtain fast and accurate reconstruction from GEGCT and to promote its system design and optimization, an in-depth investigation on a group of approximate Filtered Back-Projection (FBP) algorithms with a variety of weighting strategies has been conducted.

METHODS

The architecture of GEGCT is first presented and characterized by using a normalized-radial-offset distance (NROD). Next, shift-invariant weighted FBP-type algorithms are derived in a unified framework, with pre-filtering, filtering, and post-filtering weights, for both fixed and dynamic NROD configurations. Three viable weighting strategies are then presented including a classic one developed by Besson in the literature and two new ones generated from a curvature fitting and from an empirical formula, where all of the three weights can be expressed as certain functions of NROD. After that, an analysis of reconstruction accuracy is conducted with a wide range of NROD. Finally, the weighted FBP algorithm for GEGCT is extended to a three-dimensional form in the case of cone-beam scan with a cylindrical detector array.

RESULTS

Theoretical analysis and numerical study show that weights in the shift-invariant FBP algorithms can guarantee highly accurate reconstruction for GEGCT. A simulation of Shepp-Logan phantom and a GEGCT scan of lung mimicked by using a clinical lung CT dataset both demonstrate that FBP reconstructions with Besson and polynomial weights can achieve excellent image quality, with Peak Signal to Noise Ratio and Structural Similarity being at the same level as that from the standard equiangular fan-beam CT scan. Reconstruction of a cylinder object with multiple contrasts from simulated GEGCT scan with dynamic NROD is also highly consistent with fixed ones when using the Besson and polynomial weights, with root mean square error less than 7 hounsfield units, demonstrating the robustness and flexibility of the presented FBP algorithms. In terms of resolution, the direct FBP methods for GEGCT could achieve 1.35 lp/mm of spatial resolution at 10% modulation transfer functions point, higher than that of the rebinning method which can only reach 1.14 lp/mm. Moreover, 3D reconstructions of a disc phantom reveal that a greater value of NROD for GEGCT will bring less cone beam artifacts as expected.

CONCLUSIONS

We propose the concept of GEGCT and investigate the feasibility of using shift-invariant weighted FBP-type algorithms for reconstruction from GEGCT data without rebinning. A comprehensive analysis and phantom studies have been conducted to validate the effectiveness of proposed weighting strategies in a wide range of NROD for GEGCT with fixed and dynamic NROD.

A new weighting scheme for arc based circle cone-beam CT reconstruction

In this paper, we present an arc based fan-beam computed tomography (CT) reconstruction algorithm by applying Katsevich's helical CT image reconstruction formula to 2D fan-beam CT scanning data. Specifically, we propose a new weighting function to deal with the redundant data. Our weighting function ϖ(x_,λ) is an average of two characteristic functions, where each characteristic function indicates whether the projection data of the scanning angle contributes to the intensity of the pixel x_. In fact, for every pixel x_, our method uses the projection data of two scanning angle intervals to reconstruct its intensity, where one interval contains the starting angle and another contains the end angle. Each interval corresponds to a characteristic function. By extending the fan-beam algorithm to the circle cone-beam geometry, we also obtain a new circle cone-beam CT reconstruction algorithm. To verify the effectiveness of our method, the simulated experiments are performed for 2D fan-beam geometry with straight line detectors and 3D circle cone-beam geometry with flat-plan detectors, where the simulated sinograms are generated by the open-source software "ASTRA toolbox." We compare our method with the other existing algorithms. Our experimental results show that our new method yields the lowest root-mean-square-error (RMSE) and the highest structural-similarity (SSIM) for both reconstructed 2D and 3D fan-beam CT images.

Adaptive iterative dose reduction 3D versus filtered back projection in CT: evaluation of image quality

OBJECTIVE

The purpose of this study was to evaluate image quality with filtered back projection (FBP) and adaptive iterative dose reduction 3D (AIDR 3D).

MATERIALS AND METHODS

Phantom acquisitions were performed at six dose levels to assess spatial resolution, noise, and low-contrast detectability (LCD). Spatial resolution was assessed with the modulation transfer function at high and low contrast levels. Noise power spectrum and SD of attenuation were assessed. LCD was calculated with a mathematic model observer applied to phantom CT images. The subjective image quality of clinical CT scans was assessed by five radiologists.

RESULTS

Compared with FBP, AIDR 3D resulted in substantial noise reduction at all frequencies with a similar shape of the noise power spectrum. Spatial resolution was similar for AIDR 3D and FBP. LCD improved with AIDR 3D, which was associated with a potential average dose reduction of 36% (range, 9-86%). The observer study showed that overall image quality improved and artifacts decreased with AIDR 3D.

CONCLUSION

AIDR 3D performs better than FBP with regard to noise and LCD, resulting in better image quality, and performs similarly with respect to spatial resolution. The evaluation of image quality of clinical CT scans was consistent with the objective assessment of image quality with a phantom. The amount of dose reduction should be investigated for each clinical indication in studies with larger numbers of patients.

Dedicated breast CT: radiation dose for circle-plus-line trajectory

PURPOSE

Dedicated breast CT prototypes used in clinical investigations utilize single circular source trajectory and cone-beam geometry with flat-panel detectors that do not satisfy data-sufficiency conditions and could lead to cone beam artifacts. Hence, this work investigated the glandular dose characteristics of a circle-plus-line trajectory that fulfills data-sufficiency conditions for image reconstruction in dedicated breast CT.

METHODS

Monte Carlo-based computer simulations were performed using the GEANT4 toolkit and was validated with previously reported normalized glandular dose coefficients for one prototype breast CT system. Upon validation, Monte Carlo simulations were performed to determine the normalized glandular dose coefficients as a function of x-ray source position along the line scan. The source-to-axis of rotation distance and the source-to-detector distance were maintained constant at 65 and 100 cm, respectively, in all simulations. The ratio of the normalized glandular dose coefficient at each source position along the line scan to that for the circular scan, defined as relative normalized glandular dose coefficient (RD(g)N), was studied by varying the diameter of the breast at the chest wall, chest-wall to nipple distance, skin thickness, x-ray beam energy, and glandular fraction of the breast.

RESULTS

The RD(g)N metric when stated as a function of source position along the line scan, relative to the maximum length of line scan needed for data sufficiency, was found to be minimally dependent on breast diameter, chest-wall to nipple distance, skin thickness, glandular fraction, and x-ray photon energy. This observation facilitates easy estimation of the average glandular dose of the line scan. Polynomial fit equations for computing the RD(g)N and hence the average glandular dose are provided.

CONCLUSIONS

For a breast CT system that acquires 300-500 projections over 2π for the circular scan, the addition of a line trajectory with equal source spacing and constant x-ray beam quality (kVp and HVL) and mAs matched to the circular scan, will result in less than 0.18% increase in average glandular dose to the breast per projection along the line scan.

Accurate image reconstruction using real C-arm data from a Circle-plus-arc trajectory

OBJECTIVE

Developing an efficient tool for accurate three-dimensional imaging from projections measured with C-arm systems.

MATERIAL AND METHODS

A circle-plus-arc trajectory, which is complete and thus amenable to accurate reconstruction, is used. This trajectory is particularly attractive as its implementation does not require moving the patient. For reconstruction, we use the "M-line method", which allows processing the data in the efficient filtered backprojection mode. This method also offers the advantage of not requiring an ideal data acquisition geometry, i.e., the M-line algorithm can account for known deviations in the scanning geometry, which is important given that sizeable deviations are generally encountered in C-arm imaging.

RESULTS

A robust implementation scheme of the "M-line method" that applies straightforwardly to real C-arm data is presented. In particular, a numerically stable technique to compute the view-dependent derivative with respect to the source trajectory parameter is applied, and an efficient way to compute the π-line backprojection intervals via a polygonal weighting mask is presented. Projection data of an anthropomorphic thorax phantom were acquired on a medical C-arm scanner and used to demonstrate the benefit of using a complete data acquisition geometry with an accurate reconstruction algorithm versus using a state-of-the-art implementation of the conventional Feldkamp algorithm with a circular short scan of cone-beam data. A significant image quality improvement based on visual assessment is shown in terms of cone-beam artifacts.

Interior region-of-interest reconstruction using a small, nearly piecewise constant subregion

PURPOSE

To develop a method to reconstruct an interior region-of-interest (ROI) image with sufficient accuracy that uses differentiated backprojection (DBP) projection onto convex sets (POCS) [H. Kudo et al., "Tiny a priori knowledge solves the interior problem in computed tomography," Phys. Med. Biol. 53, 2207-2231 (2008)] and a tiny knowledge that there exists a nearly piecewise constant subregion.

METHODS

The proposed method first employs filtered backprojection to reconstruct an image on which a tiny region P with a small variation in the pixel values is identified inside the ROI. Total variation minimization [H. Yu and G. Wang, "Compressed sensing based interior tomography," Phys. Med. Biol. 54, 2791-2805 (2009); W. Han et al., "A general total variation minimization theorem for compressed sensing based interior tomography," Int. J. Biomed. Imaging 2009, Article 125871 (2009)] is then employed to obtain pixel values in the subregion P, which serve as a priori knowledge in the next step. Finally, DBP-POCS is performed to reconstruct f(x,y) inside the ROI. Clinical data and the reconstructed image obtained by an x-ray computed tomography system (SOMATOM Definition; Siemens Healthcare) were used to validate the proposed method. The detector covers an object with a diameter of approximately 500 mm. The projection data were truncated either moderately to limit the detector coverage to Ø 350 mm of the object or severely to cover Ø199 mm. Images were reconstructed using the proposed method.

RESULTS

The proposed method provided ROI images with correct pixel values in all areas except near the edge of the ROI. The coefficient of variation, i.e., the root mean square error divided by the mean pixel values, was less than 2.0% or 4.5% with the moderate or severe truncation cases, respectively, except near the boundary of the ROI.

CONCLUSIONS

The proposed method allows for reconstructing interior ROI images with sufficient accuracy with a tiny knowledge that there exists a nearly piecewise constant subregion.

A note on computing the derivative at a constant direction

The derivative at constant direction is frequently used in inversion of cone-beam data. Several algorithms for computing the derivative have been proposed in the literature. The best algorithm to date has been proposed recently by Noo et al (2007 Phys. Med. Biol. 52 5393-414). In this note we propose a new, simple and efficient formula for computing the derivative. Numerical experiments with helical CT show that our formula and the one of Noo et al provide fairly similar spatial resolution and noise stability, even though the new formula is more efficient and easier to implement.

3D analytic cone-beam reconstruction for multiaxial CT acquisitions

A conventional 3rd generation Computed Tomography (CT) system with a single circular source trajectory is limited in terms of longitudinal scan coverage since extending the scan coverage beyond 40 mm results in significant cone-beam artifacts. A multiaxial CT acquisition is achieved by combining multiple sequential 3rd generation axial scans or by performing a single axial multisource CT scan with multiple longitudinally offset sources. Data from multiple axial scans or multiple sources provide complementary information. For full-scan acquisitions, we present a window-based 3D analytic cone-beam reconstruction algorithm by tessellating data from neighboring axial datasets. We also show that multi-axial CT acquisition can extend the axial scan coverage while minimizing cone-beam artifacts. For half-scan acquisitions, one cannot take advantage of conjugate rays. We propose a cone-angle dependent weighting approach to combine multi-axial half-scan data. We compute the relative contribution from each axial dataset to each voxel based on the X-ray beam collimation, the respective cone-angles, and the spacing between the axial scans. We present numerical experiments to demonstrate that the proposed techniques successfully reduce cone-beam artifacts at very large volumetric coverage.

Motion compensated fan-beam reconstruction for nonrigid transformation

We develop an approximate fan-beam algorithm to reconstruct an object with time-dependent nonrigid transformation such as the heart. The method is in the form of derivative backprojection filtering with compensation of affine transformations on a local basis. Computer simulations showed the proposed method significantly reduces image artifact due to nonrigid motion. Therefore, with very little motion artifact, the proposed method allowed us to reconstruct images from projections over about one motion cycle, resulting in reduced image noise level down to 40% of the current level.

A factorization approach for cone-beam reconstruction on a circular short-scan

In this paper, we introduce a new algorithm for 3-D image reconstruction from cone-beam (CB) projections acquired along a partial circular scan. Our algorithm is based on a novel, exact factorization of the initial 3-D reconstruction problem into a set of independent 2-D inversion problems, each of which corresponds to finding the object density on one, single plane. Any such 2-D inversion problem is solved numerically using a projected steepest descent iteration scheme. We present a numerical evaluation of our factorization algorithm using computer-simulated CB data, without and with noise, of the FORBILD head phantom and of a disk phantom. First, we study quantitatively the impact of the reconstruction parameters on the algorithm performance. Next, we present reconstruction results for visual assessment of the achievable image quality and provide, for comparison, results obtained with two other state-of-the-art reconstruction algorithms for the circular short-scan.