Robert Lapp

Simultaneous misalignment correction for approximate circular cone-beam computed tomography

Currently, CT scanning is often performed using flat detectors which are mounted on C-arm units or dedicated gantries as in radiation therapy or micro CT. For perspective cone-beam backprojection of the Feldkamp type (FDK) the geometry of an approximately circular scan trajectory has to be available for reconstruction. If the system or the scan geometry is afflicted with geometrical instabilities, referred to as misalignment, a non-perfect approximate circular scan is the case. Reconstructing a misaligned scan without knowledge of the true trajectory results in severe artefacts in the CT images. Unlike current methods which use a pre-scan calibration of the geometry for defined scan protocols and calibration phantoms, we propose a real-time iterative restoration of reconstruction geometry by means of entropy minimization. Entropy minimization is performed combining a simplex algorithm for multi-parameter optimization and iterative graphics card (GPU)-based FDK-reconstructions. Images reconstructed with the misaligned geometry were used as an input for the entropy minimization algorithm. A simplex algorithm changes the geometrical parameters of the source and detector with respect to the reduction of entropy. In order to reduce the size of the high-dimensional space required for minimization, the trajectory was described by only eight fix points. A virtual trajectory is generated for each iteration using a least-mean-squares algorithm to calculate an approximately circular path including these points. Entropy was minimal for the ideal dataset, whereas strong misalignment resulted in a higher entropy value. For the datasets used in this study, the simplex algorithm required 64-200 iterations to achieve an entropy value equivalent to the ideal dataset, depending on the grade of misalignment using random initialization conditions. The use of the GPU reduced the time per iteration as compared to a quad core CPU-based backprojection by a factor of 10 resulting in a total of 15-20 ms per iteration, and thus providing an online geometry restoration after a total computation time of approximately 1-3 s, depending on the number of iterations. The proposed method provides accurate geometry restoration for approximately circular scans and eliminates the need for an elaborate off-line calibration for each scan. If a priori information about the trajectory is used to initialize the simplex algorithm, it is expected that the entropy minimization will converge significantly faster.

A new weighting function to achieve high temporal resolution in circular cone-beam CT with shifted detectors.

The size of the field of measurement (FOM) in computed tomography is limited by the size of the x-ray detector. In general, the detector is mounted symmetrically with respect to the rotation axis such that the transaxial FOM diameter approximately equals the lateral dimensions of the detector when being demagnified to the isocenter. To enlarge the FOM one may laterally shift the detector by up to 50% of its size. Well-known weighting functions must then be applied to the raw data prior to convolution and backprojection. In this case, a full scan or a scan with more than 360° angular coverage is required to obtain complete data. However, there is a small region, the inner FOM, that is covered redundantly and where a partial scan reconstruction may be sufficient. A new weighting function is proposed that allows one to reconstruct partial scans in that inner FOM while it reconstructs full scan or overscan data for the outer FOM, which is the part that contains no redundancies. The presented shifted detector partial scan algorithm achieves a high temporal resolution in the inner FOM while maintaining truncation-free images for the outer part. The partial scan window can be arbitrarily shifted in the angular direction, what corresponds to shifting the temporal window of the data shown in the inner FOM. This feature allows for the reconstruction of dynamic CT data with high temporal resolution. The approach presented here is evaluated using simulated and measured data for a dual source micro-CT scanner with rotating gantry.

3D/4D Cardiac Segmentation Using Active Appearance Models, Non-rigid Registration, and the Insight Toolkit

We describe the design of a statistical atlas-based 3D/4D cardiac segmentation system using a combination of active appearance models (AAM) and statistical deformation models with the Insight Toolkit as an underlying implementation framework. Since the original AAM approach was developed for 2D applications and makes use of manually set landmarks its extension to higher dimensional data sets cannot be easily achieved. We therefore apply the idea of statistical deformation models to AAMs and use a deformable registration step for establishing point-to-point correspondences. An evaluation of the implemented system was performed by segmenting the left ventricle cavity, myocardium and right ventricle of ten cardiac MRI and ten CT datasets. The comparison of automatic and manual segmentations showed encouraging results with a mean segmentation error of 2.2±1.1 mm. We conclude that the combination of a non-rigid registration step with the statistical analysis concepts of the AAM is both feasible and useful and allows for its application to 3D and 4D data.

Assessment of spatial resolution in CT

To quantify spatial resolution in CT one typically performs separate measurements for the lateral and the longitudinal point spread function (PSF). Many procedures further require reconstructions with very small voxel sizes, e.g. when wire phantoms are scanned. This, however, may already change the shape of the PSF. For example, this is the case when Moiré filters are applied or when iterative image reconstruction algorithms are used. Aiming at assessing the point spread function (PSF) and the modulation transfer function (MTF) of a CT scanner using a single measurement we propose to measure a sphere, perform a standard image reconstruction and evaluate profiles through the sphere surface. The radial symmetry of CT scanners allows to reduce the dimensionality of the PSF and the MTF from three to two by radial averaging. It is shown that the resulting two-dimensional profiles can be decomposed into a radial and into a longitudinal component by two-dimensional parallel-beam filtered backprojection. Our method was assessed using simulated and measured data of a homogeneous sphere. The measurements were performed with the capable in-vivo cone-beam micro-CT scanner VAMP TomoScope 30s. The longitudinal and radial PSFs, and the corresponding MTFs, highly agree with those obtained with conventional methods, for both the simulations and the measurements. Figures of merit extracted from the curves, such as the full width at half maximum of the PSF or the 10% value of the MTF, differ by less than 5% between the new method and the conventional approaches. Therewith it gives a technique which requires only one, easy to handle, measurement of a sphere to calculate radial and longitudinal PSF and therefrom obtain the corresponding MTFs. Furthermore it does not require a dedicated reconstruction with very small voxels. Therefore it appears superior to existing methods.

Respiratory phase-correlated micro-CT imaging of free-breathing rodents

We provide a dedicated phase-correlated imaging procedure for respiratory gating in micro-CT imaging with automatic detection of the optimal data window providing the least amount of motion blurring. A rawdata-based motion function (kymogram) was used for synchronization purposes and for identification of the optimal data window used for phase-correlated image reconstruction. Measurements were performed on a dual-source micro-CT scanner. Projection data were acquired over ten rotations for multi-segment phase-correlated reconstruction. Visual assessment was performed on datasets of ten free-breathing subjects. The kymogram approach provided a reliable synchronization signal for phase-correlated image reconstruction. Also, it allowed for the identification of phase intervals of increased and decreased motion and the corresponding detection of the optimal reconstruction phase. Phase-correlated images showed a strong improvement with respect to motion blurring compared to standard image reconstruction. A reconstruction for the calculated optimal data window provided the least amount of motion blurring and even allowed for the assessment of small structures in the lung. The dedicated retrospective phase-correlated image reconstruction procedure for respiratory gating is a feasible approach for motion-free imaging. A subject-specific optimal reconstruction phase can minimize motion blurring and further improve image quality.

Rawdata-Based detection of the optimal reconstruction phase in ECG-Gated cardiac image reconstruction

In order to achieve diagnostically useful CT (computed tomography) images of the moving heart, the standard image reconstruction has to be modified to a phase-correlated reconstruction, which considers the motion phase of the heart and generates a quasi-static image in one defined motion phase. For that purpose a synchronization signal is needed, typically a concurrent ECG recording. Commonly, the reconstruction phase is adapted by the user to the patient-specific heart motion to improve the image quality and thus the diagnostic value. The purpose of our work is to automatically identify the optimal reconstruction phase for cardiac CT imaging with respect to motion artifacts. We provide a solution for a patient- and heart rate-independent detection of the optimal phase in the cardiac cycle which shows a minimum of cardiac movement. We validated our method by the correlation with the reconstruction phase selected visually on the basis of ECG-triggering and used for the medical diagnosis. The mean difference between both reconstruction phases was 12.5% with respect to a whole cardiac motion cycle indicating a high correlation. Additionally, reconstructed cardiac images are shown which confirm the results expressed by the correlation measurement and in some cases even indicating an improvement using the proposed method.

Interactive GPU-Accelerated Image Reconstruction in Cone-Beam CT

We offer a novel approach for real-time CT reconstruction with the possibility of interactively changing parameters like the position and orientation of the slice to arbitrary values by the user during the analysis. To achieve this, a new reconstruction, including backprojection, is done every time the user wants to see a different view (in contrast to computing a volume upfront). The reconstruction was implemented on a GPU (graphics processing unit) using OpenGL and provides near real-time performance with less than 20 ms reconstruction time for 512 × 512 images. With this approach the user is free to change parameters that are fixed when a conventional reconstruction is used. So he is free to set the position of the slice, its orientation and the voxel size to arbitrary values, or to select a different set of projections for a cardiac reconstruction. Thus the waiting time for the volume reconstruction is removed. Therefore our method is esp. promising for applications such as intra-operative CT and interventional CT.

Image-based online correction of misalignment artifacts in cone-beam CT

To perform a perspective cone-beam backprojection of the Feldkamp-type (FDK) the geometry of the approximately circular scan trajectory has to be available. If the system or the scan geometry is unknown and afflicted with geometric instabilities (misalignment) reconstructing a misaligned scan can cause severe artifacts in the CT images. We propose an online and image-based iterative correction of a misaligned reconstruction geometry by using entropy minimization. Unlike current methods which use a calibration of the geometry for defined scan protocols and calibration phantoms, the proposed method is performed combining a simplex algorithm for multi-parameter optimization and a graphics card (GPU)-based FDK-reconstruction in an iterative scheme. The simplex algorithm changes the geometric parameters of source and detector with respect to the reduction of entropy. In order to reduce the size of the dimensional space required for minimization the trajectory described by a subset of trajectory points. A virtual trajectory of an approximately circular path is generated after each iteration of the algorithm. This method was validated using simulations and measurements performed on a Carm CT System equipped with a flat-panel detector (Axiom Artis, Siemens Healthcare, Forchheim, Germany). Entropy was minimal for the ideal dataset, whereas strong misalignment resulted in a higher entropy value. The use of the GPU-based reconstruction provided an online geometry correction after a total computation time of only 1-3 s using 100 to 300 iterations of the algorithm, depending on the degree of misalignment and initialization conditions.

Interactively variable isotropic resolution in computed tomography

An individual balancing between spatial resolution and image noise is necessary to fulfil the diagnostic requirements in medical CT imaging. In order to change influencing parameters, such as reconstruction kernel or effective slice thickness, additional raw-data-dependent image reconstructions have to be performed. Therefore, the noise versus resolution trade-off is time consuming and not interactively applicable. Furthermore, isotropic resolution, expressed by an equivalent point spread function (PSF) in every spatial direction, is important for the undistorted visualization and quantitative evaluation of small structures independent of the viewing plane. Theoretically, isotropic resolution can be obtained by matching the in-plane and through-plane resolution with the aforementioned parameters. Practically, however, the user is not assisted in doing so by current reconstruction systems and therefore isotropic resolution is not commonly achieved, in particular not at the desired resolution level. In this paper, an integrated approach is presented for equalizing the in-plane and through-plane spatial resolution by image filtering. The required filter kernels are calculated from previously measured PSFs in x/y- and z-direction. The concepts derived are combined with a variable resolution filtering technique. Both approaches are independent of CT raw data and operate only on reconstructed images which allows for their application in real time. Thereby, the aim of interactively variable, isotropic resolution is achieved. Results were evaluated quantitatively by measuring PSFs and image noise, and qualitatively by comparing the images to direct reconstructions regarded as the gold standard. Filtered images matched direct reconstructions with arbitrary reconstruction kernels with standard deviations in difference images of typically between 1 and 17 HU. Isotropic resolution was achieved within 5% of the selected resolution level. Processing times of 20-100 ms per frame allow for interactive use.

Cardiac phase-correlated image reconstruction and advanced image processing in pulmonary CT imaging

Image quality in pulmonary CT imaging is commonly degraded by cardiac motion artifacts. Phase-correlated image reconstruction algorithms known from cardiac imaging can reduce motion artifacts but increase image noise and conventionally require a concurrently acquired ECG signal for synchronization. Techniques are presented to overcome these limitations. Based on standard and phase-correlated images that are reconstructed using a raw data-derived synchronization signal, image-merging and temporal-filtering techniques are proposed that combine the input images automatically or interactively. The performance of the approaches is evaluated in patient and phantom datasets. In the automatic approach, areas of strong motion and static areas were well detected, providing an optimal combination of standard and phase-correlated images with no visible border between the merged regions. Image noise in the non-moving regions was reduced to the noise level of the standard reconstruction. The application of the interactive filtering allowed for an optimal adaptation of image noise and motion artifacts. Noise content after interactive filtering decreased with increasing temporal filter width used. We conclude that a combination of our motion-free merging approach and a dedicated interactive filtering procedure can highly improve pulmonary imaging with respect to motion artifacts and image noise.