Calibration-free beam hardening reduction in x-ray CBCT using the epipolar consistency condition and physical constraints.

BACKGROUND: The beam hardening effect is a typical source of artifacts in x-ray cone beam computed tomography (CBCT). It causes streaks in reconstructions and corrupted Hounsfield units toward the center of objects, widely known as cupping artifacts. PURPOSE: We present a novel efficient projection data-based method for reduction of beam-hardening artifacts and incorporate physical constraints on the shape of the compensation functions. The method is calibration-free and requires no additional knowledge of the scanning setup. METHOD: The mathematical model of the beam hardening effect caused by a single material is analyzed. We show that the effect of beam hardening on the resulting functions on the line integral measurements are monotonous and concave functions of the ideal data. This holds irrespective of any limiting assumptions on the energy dependency of the material, the detector response or properties of the x-ray source. A regression model for the beam hardening effect respecting these theoretical restrictions is proposed. Subsequently, we present an efficient method to estimate the parameters of this model directly in projection domain using an epipolar consistency condition. Computational efficiency is achieved by exploiting the linearity of an intermediate function in the formulation of our optimization problem. RESULTS: Our evaluation shows that the proposed physically constrained ECC 2 algorithm is effective even in challenging measured data scenarios with additional sources of inconsistency. CONCLUSIONS: The combination of mathematical consistency condition and a compensation model that is based on the properties of x-ray physics enables us to improve image quality of measured data retrospectively and to decrease the need for calibration in a data-driven manner.

Prior-Free Respiratory Motion Estimation in Rotational Angiography.

Rotational coronary angiography using C-arm angiography systems enables intra-procedural 3-D imaging that is considered beneficial for diagnostic assessment and interventional guidance. Despite previous efforts, rotational angiography was not yet successfully established in clinical practice for coronary artery procedures due to challenges associated with substantial intra-scan respiratory and cardiac motion. While gating handles cardiac motion during reconstruction, respiratory motion requires compensation. State-of-the-art algorithms rely on 3-D / 2-D registration that requires an uncompensated reconstruction of sufficient quality. To overcome this limitation, we investigate two prior-free respiratory motion estimation methods based on the optimization of: 1) epipolar consistency conditions (ECCs) and 2) a task-based auto-focus measure (AFM). The methods assess redundancies in projection images or impose favorable properties of 3-D space, respectively, and are used to estimate the respiratory motion of the coronary arteries within rotational angiograms. We evaluate our algorithms on the publicly available CAVAREV benchmark and on clinical data. We quantify reductions in error due to respiratory motion compensation using a dedicated reconstruction domain metric. Moreover, we study the improvements in image quality when using an analytic and a novel temporal total variation regularized algebraic reconstruction algorithm. We observed substantial improvement in all figures of merit compared with the uncompensated case. Improvements in image quality presented as a reduction of double edges, blurring, and noise. Benefits of the proposed corrections were notable even in cases suffering little corruption from respiratory motion, translating to an improvement in the vessel sharpness of (6.08 ± 4.46)% and (14.7 ± 8.80)% when the ECC-based and the AFM-based compensation were applied. On the CAVAREV data, our motion compensation approach exhibits an improvement of (27.6 ± 7.5)% and (97.0 ± 17.7)% when the ECC and AFM were used, respectively. At the time of writing, our method based on AFM is leading the CAVAREV scoreboard. Both motion estimation strategies are purely image-based and accurately estimate the displacements of the coronary arteries due to respiration. While current evidence suggests the superior performance of AFM, future work will further investigate the use of ECC in the context of angiography as they solely rely on geometric calibration and projection-domain images.

Consistency-based respiratory motion estimation in rotational angiography.

PURPOSE: Rotational coronary angiography enables 3D reconstruction but suffers from intra-scan cardiac and respiratory motion. While gating handles cardiac motion, respiratory motion requires compensation. State-of-the-art algorithms rely on 3D-2D registration that depends on initial reconstructions of sufficient quality. We propose a compensation method that is applied directly in projection domain. It overcomes the need for reconstruction and thus complements the state-of-the-art. METHODS: Virtual single-frame background subtraction based on vessel segmentation and spectral deconvolution yields non-truncated images of the contrasted lumen. This allows motion compensation based on data consistency conditions. We compensate craniocaudal shifts by optimizing epipolar consistency to (a) devise an image-based surrogate for cardiac motion and (b) compensate for respiratory motion. We validate our approach in two numerical phantom studies and three clinical cases. RESULTS: Correlation of the image-based surrogate for cardiac motion with the ECG-based ground truth was excellent yielding a Pearson correlation of 0.93 ± 0.04. Considering motion compensation, the target error measure decreased by 98% and 69%, respectively, for the phantom experiments while for the clinical cases the same figure of merit improved by 46 ± 21%. CONCLUSIONS: The proposed method is entirely image-based and accurately estimates craniocaudal shifts due to respiration and cardiac contraction. Future work will investigate experimental trajectories and possibilities for simplification of the single-frame subtraction pipeline.

An Improved Extrapolation Scheme for Truncated CT Data Using 2D Fourier-Based Helgason-Ludwig Consistency Conditions.

We improve data extrapolation for truncated computed tomography (CT) projections by using Helgason-Ludwig (HL) consistency conditions that mathematically describe the overlap of information between projections. First, we theoretically derive a 2D Fourier representation of the HL consistency conditions from their original formulation (projection moment theorem), for both parallel-beam and fan-beam imaging geometry. The derivation result indicates that there is a zero energy region forming a double-wedge shape in 2D Fourier domain. This observation is also referred to as the Fourier property of a sinogram in the previous literature. The major benefit of this representation is that the consistency conditions can be efficiently evaluated via 2D fast Fourier transform (FFT). Then, we suggest a method that extrapolates the truncated projections with data from a uniform ellipse of which the parameters are determined by optimizing these consistency conditions. The forward projection of the optimized ellipse can be used to complete the truncation data. The proposed algorithm is evaluated using simulated data and reprojections of clinical data. Results show that the root mean square error (RMSE) is reduced substantially, compared to a state-of-the-art extrapolation method.

Epipolar Consistency in Transmission Imaging.

This paper presents the derivation of the Epipolar Consistency Conditions (ECC) between two X-ray images from the Beer-Lambert law of X-ray attenuation and the Epipolar Geometry of two pinhole cameras, using Grangeat's theorem. We motivate the use of Oriented Projective Geometry to express redundant line integrals in projection images and define a consistency metric, which can be used, for instance, to estimate patient motion directly from a set of X-ray images. We describe in detail the mathematical tools to implement an algorithm to compute the Epipolar Consistency Metric and investigate its properties with detailed random studies on both artificial and real FD-CT data. A set of six reference projections of the CT scan of a fish were used to evaluate accuracy and precision of compensating for random disturbances of the ground truth projection matrix using an optimization of the consistency metric. In addition, we use three X-ray images of a pumpkin to prove applicability to real data. We conclude, that the metric might have potential in applications related to the estimation of projection geometry. By expression of redundancy between two arbitrary projection views, we in fact support any device or acquisition trajectory which uses a cone-beam geometry. We discuss certain geometric situations, where the ECC provide the ability to correct 3D motion, without the need for 3D reconstruction.

Denoising and artefact reduction in dynamic flat detector CT perfusion imaging using high speed acquisition: first experimental and clinical results.

Flat detector CT perfusion (FD-CTP) is a novel technique using C-arm angiography systems for interventional dynamic tissue perfusion measurement with high potential benefits for catheter-guided treatment of stroke. However, FD-CTP is challenging since C-arms rotate slower than conventional CT systems. Furthermore, noise and artefacts affect the measurement of contrast agent flow in tissue. Recent robotic C-arms are able to use high speed protocols (HSP), which allow sampling of the contrast agent flow with improved temporal resolution. However, low angular sampling of projection images leads to streak artefacts, which are translated to the perfusion maps. We recently introduced the FDK-JBF denoising technique based on Feldkamp (FDK) reconstruction followed by joint bilateral filtering (JBF). As this edge-preserving noise reduction preserves streak artefacts, an empirical streak reduction (SR) technique is presented in this work. The SR method exploits spatial and temporal information in the form of total variation and time-curve analysis to detect and remove streaks. The novel approach is evaluated in a numerical brain phantom and a patient study. An improved noise and artefact reduction compared to existing post-processing methods and faster computation speed compared to an algebraic reconstruction method are achieved.

On the energetics of conformational switching of molecules at and close to room temperature.

We observe and induce conformational switching of individual molecules via scanning tunneling microscopy (STM) at and close to room temperature. 2H-5,10,15,20-Tetrakis-(3,5-di-tert-butyl)-phenylporphyrin adsorbed on Cu(111) forms a peculiar supramolecular ordered phase in which the molecules arrange in alternating rows, with two distinct appearances in STM which are assigned to concave and convex intramolecular conformations. Around room temperature, frequent bidirectional conformational switching of individual molecules from concave to convex and vice versa is observed. From the temperature dependence, detailed insights into the energy barriers and entropic contributions of the switching processes are deduced. At 200 K, controlled STM tip-induced unidirectional switching is possible, yielding an information storage density of 4.9 × 10(13) bit/inch(2). With this contribution we demonstrate that controlled switching of individual molecules at comparably high temperatures is possible and that entropic effects can be a decisive factor in potential molecular devices at these temperatures.

Image-based tracking of the teeth for orthodontic augmented reality.

We present image-based methods for tracking teeth in a video image with respect to a CT scan of the jaw, in order to enable a novel light-weight augmented reality (AR) system in orthodontistry. Its purpose is guided bracket placement in orthodontic correction. In this context, our goal is to determine the position of the patient maxilla and mandible in a video image solely based on a CT scan. This is suitable for image guidance through an overlay of the video image with the planned position of brackets in a monocular AR system. Our tracking algorithm addresses the contradicting requirements of robustness, accuracy and performance in two problem-specific formulations. First, we exploit a distance-based modulation of two iso-surfaces from the CT image to approximate the appearance of the gum line. Second, back-projection of previous video frames to an iso-surface is used to account for recently placed brackets. In combination, this novel algorithm allowed us to track several sequences of three patient videos of real procedures, despite difficult lighting conditions. Paired with a systematic evaluation, we were able to show practical feasibility of such a system.

Interactive 3D visualization of a single-view X-ray image.

In this paper, we present an interactive X-Ray perceptual visualization technique (IXPV) to improve 3D perception in standard single-view X-Ray images. Based on a priori knowledge from CT data, we re-introduce lost depth information into the original single-view X-Ray image without jeopardizing information of the original X-Ray. We propose a novel approach that is suitable for correct fusion of intraoperative X-Ray and ultrasound, co-visualization of X-Ray and surgical tools, and for improving the 3D perception of standard radiographs. Phantom and animal cadaver datasets were used during experimentation to demonstrate the impact of our technique. Results from a questionnaire completed by 11 clinicians and computer scientists demonstrate the added value of introduced depth cues directly in an X-Ray image. In conclusion, we propose IXPV as a futuristic alternative to the standard radiographic image found in today's clinical setting.