Guenter Lauritsch

Theoretical framework for filtered back projection in tomosynthesis

Tomosynthesis provides only incomplete 3D-data of the imaged object. Therefore it is important for reconstruction tasks to take all available information carefully into account. We are focusing on geometrical aspects of the scan process which can be incorporated into reconstruction algorithms by filtered backprojection methods. Our goal is a systematic approach to filter design. A unified theory of tomosynthesis is derived in the context of linear system theory, and a general four-step filter design concept is presented. Since the effects of filtering are understandable in this context, a methodical formulation of filter functions is possible in order to optimize image quality regarding the specific requirements of any application. By variation of filter parameters the slice thickness and the spatial resolution can easily be adjusted. The proposed general concept of filter design is exemplarily discussed for circular scanning but is valid for any specific scan geometry. The inherent limitations of tomosynthesis are pointed out and strategies for reducing the effects of incomplete sampling are developed. Results of a dental application show a striking improvement in image quality.

Cardiac C-Arm CT: A Unified Framework for Motion Estimation and Dynamic CT

Generating 3-D images of the heart during interventional procedures is a significant challenge. In addition to real time fluoroscopy, angiographic C-arm systems can also now be used to generate 3-D/4-D CT images on the same system. One protocol for cardiac CT uses ECG triggered multisweep scans. A 3-D volume of the heart at a particular cardiac phase is then reconstructed by applying Feldkamp (FDK) reconstruction to the projection images with retrospective ECG gating. In this work we introduce a unified framework for heart motion estimation and dynamic cone-beam reconstruction using motion corrections. The benefits of motion correction are 1) increased temporal and spatial resolution by removing cardiac motion which may still exist in the ECG gated data sets and 2) increased signal-to-noise ratio (SNR) by using more projection data than is used in standard ECG gated methods. Three signal-enhanced reconstruction methods are introduced that make use of all of the acquired projection data to generate a 3-D reconstruction of the desired cardiac phase. The first averages all motion corrected back-projections; the second and third perform a weighted averaging according to 1) intensity variations and 2) temporal distance relative to a time resolved and motion corrected reference FDK reconstruction. In a comparison study seven methods are compared: nongated FDK, ECG-gated FDK, ECG-gated, and motion corrected FDK, the three signal-enhanced approaches, and temporally aligned and averaged ECG-gated FDK reconstructions. The quality measures used for comparison are spatial resolution and SNR. Evaluation is performed using phantom data and animal models. We show that data driven and subject-specific motion estimation combined with motion correction can decrease motion-related blurring substantially. Furthermore, SNR can be increased by up to 70% while maintaining spatial resolution at the same level as is provided by the ECG-gated FDK. The presented framework provides excellent image quality for cardiac C-arm CT.

Exact (spiral+circles) scan region-of-interest cone beam reconstruction via backprojection

The authors present a (spiral + circles) scan cone beam reconstruction algorithm in which image reconstruction proceeds via backprojection in the object space. In principle, the algorithm can reconstruct sectional region-of-interest (ROI) in a long object. The approach is a generalization of the cone beam backprojection technique developed by Kudo and Saito (1994) in two aspects: the resource-demanding normalization step in the Kudo and Saitos algorithm is eliminated through the technique of data combination that the authors published earlier, and the elimination of the restriction that the detector be big enough to capture the entire cone beam projection of the ROI. Restricting the projection data to the appropriate angular range required by data combination can be accomplished by a masking process. Because of the simplification resulting from the elimination of the normalization step, the most time-consuming operations of the algorithm can be approximated by the efficient step of line-by-line ramp filtering the cone beam image in the direction of the scan path, plus a correction image. The correction image, which can be computed exactly, is needed because data combination is not properly matched at the mask boundary when ramp filtering is involved. Empirical two-dimensional (2-D) point spread function (PSF) is developed to improve matching with the correction image which is computed with finite samplings. The use of transition region to further improve matching is introduced. The results of testing the algorithm on simulated phantoms are presented.

New X-ray imaging modalities and their integration with intravascular imaging and interventions

During recent years various techniques emerged providing more detailed images and insights in the cardiovascular system. C-Arm computed tomography is currently introduced in cardiac imaging offering the potential of three dimensional imaging of the coronary arteries, the cardiac chambers, venous system and a variety of anatomic anomalies inside the interventional environment. Furthermore it might enable perfusion imaging during percutaneous coronary intervention (PCI). Intravascular ultrasound (IVUS) and optical coherence tomography (OCT) are meanwhile established tools for detailed assessment of the coronary arteries. Their use might further increase with automated tissue characterization, three dimensional reconstruction, integration in angiography systems, and new emerging techniques. Parameters of fluid tissue interactions are important factors in the pathogenesis of atherosclerosis. These parameters can be calculated using computational fluid dynamics based on three dimensional models of the coronary vessels which can be derived from various sources including mulitslice computed tomography (MSCT), C-Arm CT or 3D reconstructed IVUS or OCT. Their use in the clinical setting has yet to be determined especially with regard to their ability in increasing treatment efficiency and clinical outcome.

Exact local regions-of-interest reconstruction in spiral cone-beam filtered-backprojection CT: numerical implementation and first image results

In the long object problem it is intended to reconstruct exactly a region-of-interest (ROI) of an object from spiral cone beam data which covers the ROI and its nearest vicinity only. In the first paper in a series of two the theory of the local ROI method is derived using the filtered-backprojection approach. In the present second paper the demanding numerical implementation is described. The straightforward 4-step algorithm is applied. It mainly consists of explicit calculations of the derivatives of partial plane integrals of the object from line segments in the projection images. In the local ROI method grouping of line segments to particular (phi) -planes in 3-D Radon space is important. A rigorous grouping causes artifacts which can be avoided by a fuzzy correspondence of line segments to (phi) -planes. In the ROI the same image quality is achieved for a partial scan as for a full scan. However, the method suffers from high computational requirements. The filtering step can be speeded up by replacing the 4-step algorithm by convolution with spatially variant 1-D Hilbert transforms. An in-depth analysis of the empirical PSF of detector pixels filtered by the 4-step algorithm confirmed the theoretical results. Modifications for practical implementation are outlined which are subject to further investigations.© (2000) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

A temporal interpolation approach for dynamic reconstruction in perfusion CT

This article presents a dynamic CT reconstruction algorithm for objects with time dependent attenuation coefficient. Projection data acquired over several rotations are interpreted as samples of a continuous signal. Based on this idea, a temporal interpolation approach is proposed which provides the maximum temporal resolution for a given rotational speed of the CT scanner. Interpolation is performed using polynomial splines. The algorithm can be adapted to slow signals, reducing the amount of data acquired and the computational cost. A theoretical analysis of the approximations made by the algorithm is provided. In simulation studies, the temporal interpolation approach is compared with three other dynamic reconstruction algorithms based on linear regression, linear interpolation, and generalized Parker weighting. The presented algorithm exhibits the highest temporal resolution for a given sampling interval. Hence, our approach needs less input data to achieve a certain quality in the reconstruction than the other algorithms discussed or, equivalently, less x-ray exposure and computational complexity. The proposed algorithm additionally allows the possibility of using slow rotating scanners for perfusion imaging purposes.

Evaluation and empirical analysis of an exact FBP algorithm for spiral cone-beam CT

Recently one of the authors proposed a reconstruction algorithm, which is theoretically exact and has the truly shift-invariant filtering and backprojection structure. Each voxel is reconstructed using the theoretically minimum section of the spiral, which is located between the endpoints of the PI segment of the voxel. Filtering is one-dimensional, performed along lines with variable tilt on the detector, and consists of five terms. We will present evaluation of the performance of the algorithm. We will also discuss and illustrate empirically the contributions of the five filtering terms to the overall image. A thorough evaluation proved the validity of the algorithm. Excellent image results were achieved even for high pitch values. Overall image quality can be regarded as at least equivalent to the less efficient, exact, Radon-based methods. However, the new algorithm significantly increases efficiency. Thus, the method has the potential to be applied in clinical scanners of the future. The empirical analysis leads to a simple, intuitive understanding of the otherwise obscure terms of the algorithm. Identification and skipping of the practically irrelevant fifth term allows significant speed-up of the algorithm due to uniform distance weighting.

Back-projection spiral scan region-of-interest cone beam CT

We present a spiral scan cone beam reconstruction algorithm in which image reconstruction proceeds via backprojection in the object space. In principle the algorithm can reconstruct sectional ROI in a long object. The approach is a generalization of the cone beam backprojection technique developed by Kudo and Saito in two aspects: the resource- demanding normalization step in the Kudo and Saitos algorithm is eliminated through the technique of data combination which we published earlier, and the elimination of the restriction that the detector be big enough to capture the entire image of the ROI. Restricting the projection data to the appropriate angular range required by data combination can be accomplished by a masking process. The mask consists of a top curve and a bottom curve formed by projecting the spiral turn above and the turn below from the current source position. Because of the simplification resulting from the elimination of the normalization step, the most time-consuming operations of the algorithm can be approximated by the efficient step of line-by-line ramp filtering the cone beam image in the direction of the scan path, plus a correction term. The correction term is needed because data combination is not properly matched at the mask boundary when ramp filtering is involved. This correction term to the mask boundary effect can be computed exactly. The results of testing the algorithm on simulated phantoms are presented.

Evaluation of interpolation methods for surface-based motion compensated tomographic reconstruction for cardiac angiographic C-arm data

PURPOSE For interventional cardiac procedures, anatomical and functional information about the cardiac chambers is of major interest. With the technology of angiographic C-arm systems it is possible to reconstruct intraprocedural three-dimensional (3D) images from 2D rotational angiographic projection data (C-arm CT). However, 3D reconstruction of a dynamic object is a fundamental problem in C-arm CT reconstruction. The 2D projections are acquired over a scan time of several seconds, thus the projection data show different states of the heart. A standard FDK reconstruction algorithm would use all acquired data for a filtered backprojection and result in a motion-blurred image. In this approach, a motion compensated reconstruction algorithm requiring knowledge of the 3D heart motion is used. The motion is estimated from a previously presented 3D dynamic surface model. This dynamic surface model results in a sparse motion vector field (MVF) defined at control points. In order to perform a motion compensated reconstruction, a dense motion vector field is required. The dense MVF is generated by interpolation of the sparse MVF. Therefore, the influence of different motion interpolation methods on the reconstructed image quality is evaluated. METHODS Four different interpolation methods, thin-plate splines (TPS), Shepards method, a smoothed weighting function, and a simple averaging, were evaluated. The reconstruction quality was measured on phantom data, a porcine model as well as on in vivo clinical data sets. As a quality index, the 2D overlap of the forward projected motion compensated reconstructed ventricle and the segmented 2D ventricle blood pool was quantitatively measured with the Dice similarity coefficient and the mean deviation between extracted ventricle contours. For the phantom data set, the normalized root mean square error (nRMSE) and the universal quality index (UQI) were also evaluated in 3D image space. RESULTS The quantitative evaluation of all experiments showed that TPS interpolation provided the best results. The quantitative results in the phantom experiments showed comparable nRMSE of ≈0.047 ± 0.004 for the TPS and Shepards method. Only slightly inferior results for the smoothed weighting function and the linear approach were achieved. The UQI resulted in a value of ≈ 99% for all four interpolation methods. On clinical human data sets, the best results were clearly obtained with the TPS interpolation. The mean contour deviation between the TPS reconstruction and the standard FDK reconstruction improved in the three human cases by 1.52, 1.34, and 1.55 mm. The Dice coefficient showed less sensitivity with respect to variations in the ventricle boundary. CONCLUSIONS In this work, the influence of different motion interpolation methods on left ventricle motion compensated tomographic reconstructions was investigated. The best quantitative reconstruction results of a phantom, a porcine, and human clinical data sets were achieved with the TPS approach. In general, the framework of motion estimation using a surface model and motion interpolation to a dense MVF provides the ability for tomographic reconstruction using a motion compensation technique.

Automatic extraction of 3d dynamic left ventricle model from 2d rotational angiocardiogram

In this paper, we propose an automatic method to directly extract 3D dynamic left ventricle (LV) model from sparse 2D rotational angiocardiogram (each cardiac phase contains only five projections). The extracted dynamic model provides quantitative cardiac function for analysis. The overlay of the model onto 2D real-time fluoroscopic images provides valuable visual guidance during cardiac intervention. Though containing severe cardiac motion artifacts, an ungated CT reconstruction is used in our approach to extract a rough static LV model. The initialized LV model is projected onto each 2D projection image. The silhouette of the projected mesh is deformed to match the boundary of LV blood pool. The deformation vectors of the silhouette are back-projected to 3D space and used as anchor points for thin plate spline (TPS) interpolation of other mesh points. The proposed method is validated on 12 synthesized datasets. The extracted 3D LV meshes match the ground truth quite well with a mean point-to-mesh error of 0.51 +/- 0.11 mm. The preliminary experiments on two real datasets (included a patient and a pig) show promising results too.