Harald Schöndube

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.

Evaluation of a novel CT image reconstruction algorithm with enhanced temporal resolution

We present an evaluation of a novel algorithm that is designed to enhance temporal resolution in CT beyond the short-scan limit by making use of a histogram constraint. A minimum scan angle of 180° plus fan angle is needed to acquire complete data for reconstructing an image. Conventionally, this means that a temporal resolution of half the gantry rotation time is achievable in the isocenter and that an enhancement of temporal resolution can only be accomplished by a faster gantry rotation or by using a dual-source system. In this work we pursue a different approach, namely employing an iterative algorithm to reconstruct images from less than 180° of projections and using a histogram constraint to prevent the occurrence of limited-angle artifacts. The method is fundamentally different from previously published approaches using prior images and TV minimization. Furthermore, motion detection is used to enhance dose usage in those parts of the image where temporal resolution is not critical. We evaluate the technique with patient and phantom scans as well as using simulated data. The proposed method yields good results and image quality, both with simulated and with clinical data. Our evaluations show that an enhancement of temporal resolution to a value equivalent to about 120° of projections is viable, which corresponds to an enhancement of temporal resolution by about 30%. Furthermore, by employing motion detection, a substantial noise reduction can be achieved in those parts of the image where no motion occurs.

Accurate helical cone-beam CT reconstruction with redundant data

We present a new image reconstruction algorithm for helical cone-beam computed tomography (CT). This algorithm is designed for data collected at or near maximum pitch, and provides a theoretically exact and stable reconstruction while beneficially using all measured data. The main operations involved are a differentiated backprojection and a finite-support Hilbert transform inversion. These operations are applied onto M-lines, and the beneficial use of all measured data is gained from averaging three volumes reconstructed each with a different choice of M-lines. The technique is overall similar to that presented by one of the authors in a previous publication, but operates volume-wise, instead of voxel-wise, which yields a significantly more efficient reconstruction procedure. The algorithm is presented in detail. Also, preliminary results from computer-simulated data are provided to demonstrate the numerical stability of the algorithm, the beneficial use of redundant data and the ability to process data collected with an angular flying focal spot.

Temporal resolution and motion artifacts in single-source and dual-source cardiac CT

PURPOSE The temporal resolution of a given image in cardiac computed tomography (CT) has so far mostly been determined from the amount of CT data employed for the reconstruction of that image. The purpose of this paper is to examine the applicability of such measures to the newly introduced modality of dual-source CT as well as to methods aiming to provide improved temporal resolution by means of an advanced image reconstruction algorithm. METHODS To provide a solid base for the examinations described in this paper, an extensive review of temporal resolution in conventional single-source CT is given first. Two different measures for assessing temporal resolution with respect to the amount of data involved are introduced, namely, either taking the full width at half maximum of the respective data weighting function (FWHM-TR) or the total width of the weighting function (total TR) as a base of the assessment. Image reconstruction using both a direct fan-beam filtered backprojection with Parker weighting as well as using a parallel-beam rebinning step are considered. The theory of assessing temporal resolution by means of the data involved is then extended to dual-source CT. Finally, three different advanced iterative reconstruction methods that all use the same input data are compared with respect to the resulting motion artifact level. For brevity and simplicity, the examinations are limited to two-dimensional data acquisition and reconstruction. However, all results and conclusions presented in this paper are also directly applicable to both circular and helical cone-beam CT. RESULTS While the concept of total TR can directly be applied to dual-source CT, the definition of the FWHM of a weighting function needs to be slightly extended to be applicable to this modality. The three different advanced iterative reconstruction methods examined in this paper result in significantly different images with respect to their motion artifact level, despite exactly the same amount of data being used in the reconstruction process. CONCLUSIONS The concept of assessing temporal resolution by means of the data employed for reconstruction can nicely be extended from single-source to dual-source CT. However, for advanced (possibly nonlinear iterative) reconstruction algorithms the examined approach fails to deliver accurate results. New methods and measures to assess the temporal resolution of CT images need to be developed to be able to accurately compare the performance of such algorithms.

Comparative evaluation of linear interpolation models foriterative reconstruction in X-ray CT

The forward projection operator is a key component of every iterative reconstruction method in X-ray computed tomography (CT). Besides the choices being made in the definition of the objective function and associated constraints, the forward projection model affects both bias and noise properties of the reconstruction. In this work, we compare three important forward projection models that rely on linear interpolation: the Joseph method, the distance-driven method, and the image representation using B-splines of order n = 1. The comparison focuses on bias and noise in the image as a function of the resolution. X-ray CT data that are simulated in fan-beam geometry with two different magnification factors are used.

Iterative CT reconstruction with small pixel size: distance-driven forward projector versus Joseph's

Over the last few years, iterative reconstruction methods have become an important research topic in x-ray CT imaging. This effort is motivated by increasing evidence that such methods may enable significant savings in terms of dose imparted to the patient. Conceptually, iterative reconstruction methods involve two important ingredients: the statistical model, which includes the forward projector, and a priori information in the image domain, which is expressed using a regularizer. Most often, the image pixel size is chosen to be equal (or close) to the detector pixel size (at field-of-view center). However, there are applications for which a smaller pixel size is desired. In this investigation, we focus on reconstruction with a pixel size that is twice smaller than the detector pixel size. Using such a small pixel size implies a large increase in computational effort when using the distance-driven method for forward projection, which models the detector size. On the other hand, the more efficient method of Joseph will create imbalances in the reconstruction of each pixel, in the sense that there will be large differences in the way each projection contributes to the pixels. The purpose of this work is to evaluate the impact of these imbalances on image quality in comparison with utilization of the distance-driven method. The evaluation involves computational effort, bias and noise metrics, and LROC analysis using human observers. The results show that Josephs method largely remains attractive.

Can motion compensated reconstruction improve 'best phase' reconstruction in Cardiac CT?

Based on a phantom study with a realistic coronary vessel phantom, we investigated if motion compensated cardiac CT reconstruction can improve best phase image quality with respect to motion artifacts and patency of coronary vessel lumen. Basically, tracking based methods (with and without improvement of temporal resolution) deriving the motion fields by a registration-like procedure are compared to optimization based methods optimizing objective functions while minimizing artifact levels (e.g. Motion Artifact Metric Optimization (MAM) Reconstruction). Using the MAM technique, the motion field is iteratively calculated with a steepest descent update equation minimizing a motion artifact metric. We evaluated patency of the vessel lumen, the normalized cross correlation (NCC) of the respective reconstruction data with the ground truth data and a best phase improvement index correlating the motion compensated reconstruction data to the non-compensated FDK-based reconstruction data. It will be shown that the MAM technique is superior to the tracking methods. The latter proved to be more or less susceptible to template matching and, or erroneous template size. The value of MAM is also demonstrated evaluating clinical data. In particular it is beneficial for patients with high heart rates as well as for dose optimized scan protocols because it does not need over-radiation.

Image representation using mollified pixels for iterative reconstruction in x-ray CT

We introduce a new basis function, the mollified pixel, for image representation in X-ray computed tomography and other imaging modalities. The mollified pixel is defined as the convolution of a classical pixel with a smooth function that approximates the Dirac impulse. Since such a smooth function can be defined in an infinite number of ways, the mollified pixel defines a wide class of methods for image representation. For utilization of the mollified pixel in iterative reconstruction, it is needed to know the Radon transform of a mollified pixel. Using a link between classical pixels and B-splines, we suggest a computationally-efficient expression for this Radon transform. Preliminary iterative CT reconstruction results based on mollified pixels are provided along with our theoretical developments to demonstrate the potential benefits of mollified pixels.

Accurate helical CT reconstruction with redundant data using nutating slices

We present an efficient two-step Hilbert reconstruction method working on M-lines which allows for mathematical accurate reconstruction using all the data on a standard cylindrical detector at maximum pitch. We give an overview over the problem of exact reconstruction using redundant data, describe the algorithm in detail and present results showing a notable reduction of image noise over algorithms which do not use redundant data, without compromising resolution.

Iterative CT reconstruction using coordinate descent with ordered subsets of data

Image reconstruction based on iterative minimization of a penalized weighted least-square criteria has become an important topic of research in X-ray computed tomography. This topic is motivated by increasing evidence that such a formalism may enable a significant reduction in dose imparted to the patient while maintaining or improving image quality. One important issue associated with this iterative image reconstruction concept is slow convergence and the associated computational effort. For this reason, there is interest in finding methods that produce approximate versions of the targeted image with a small number of iterations and an acceptable level of discrepancy. We introduce here a novel method to produce such approximations: ordered subsets in combination with iterative coordinate descent. Preliminary results demonstrate that this method can produce, within 10 iterations and using only a constant image as initial condition, satisfactory reconstructions that retain the noise properties of the targeted image.