Computed Tomography (CT) has become very important for industrial applications. The fields of application are ranging from highly specialized tasks in CT inline inspection to universal X-ray systems, metrology and highresolution CT, for example in microelectronics. For high-energy scans of high quality fan-beam CT using linear detector arrays (LDA) is the right choice due to the bigger field of view and the superior collimation reducing scatter artefacts compared to flat panel detectors, which are used for cone-beam CT. The conventional filtered back projection (FBP) as reconstruction algorithm requires equally spaced X-rays, i.e. it was designed for parallel beam geometry. Its computational effort depends mainly on the size of the reconstructed volume. In this article we will introduce a fast and analytical exact reconstruction algorithm, based on the orthogonal polynomial expansion on the disk (OPED). Its numerical complexity only depends on the amount of the input data (projections). OPED is designed to overcome aliasing artefacts and streaks. It needs no special filtering, i.e. it can be easily parameterized. The alignment of the sample grid is very well suited for fan beam geometry with its non-equally spaced X-rays. As result, we will compare the performance of the OPED and FBP algorithm.

The task of determining the geometry of a cone-beam CT scanner with flat panel detector and circular/spiral source trajectory is considered. Accomplishing this task implies analyzing projections of a set of points referred to as calibrating set or calibrating phantom. We take advantage of the fact that observed coordinates of a point’s projection are rational functions of the point’s location. Unknown coefficients of these functions can be recovered exactly from six projections of the point. Location of the source as well as position and orientation of the detector are determined in the scanner reference frame, which is constituted by rotation axis and central plane of the scanner. Two different projections of a calibrating set are enough to solve the task if the source trajectory is a circle. In applications where a shift of an object transversally to the central plane is required, two additional projections have to be collected in order to identify the direction of the shift. The developed formalism becomes especially simple when the detector is aligned with the rotation axis. In this case four projections of a single calibrating point rotated successfully about the rotation axis are sufficient. The error analysis carried out in the paper shows that the magnitude of deviation from the true values is of the order of the magnitude of measurement errors.

A novel fourth generation micro-CT (WATCH-CT) with a unique scanning geometry, that collects parallel projections from a standard x-ray source without the requirement to interpolate or rebin the data, is studied and evaluated for its imaging qualities and performance characteristics. For a comparative analysis of the WATCH micro-CT system and the conventional CT geometry, the local noise power spectrum and the modulation transfer function is derived from the same initial parameters. The spatial resolution (MTF), characterized by the response of the system, is determined by the MTF derived by the oversampling method. The calculations involve varying the parameters like the region of evaluation (ROE) position, FOV magnification, angular sampling, pixel size, filtration and reconstruction algorithm to provide an extensive analogy between these systems. The spatial resolution of the scanning geometries is evaluated and compared. The MTF curves illustrate a higher relative resolving capacity for the WATCH micro-CT compared to the conventional geometries which is due to the characteristics of this unique geometry. The WATCH system exhibits higher resolutions explicitly at the regions away from the center. The NPS curves of WATCH geometry shows higher noise content in comparison to the conventional geometry.

A new and simple object for calibrating tomographic scanners has been proposed. Instead of a conventional high-density ball as an object for calibration, we propose a high-density conic body. The cone is advantageous compare to the ball both because of its easy availability (uncomplicated manufacturing) and the straightforward and less error-prone analysis necessary for the identification of a space point (ball’s center vs. cone apex). Applying the conic body instead of a ball as a calibration object enables to reduce calibration errors substantially. Additionally we propose an efficient way to determine the discrepancy between ideal and misaligned positions of the detector that may be crucial for the quality of the reconstruction.

The performance of a novel designed x-ray CT scanning geometry is investigated. Composed of a specially designed tungsten collimation mask and a high resolution flat panel detector, this scanning geometry provides high efficient data acquisition allowing dose reduction potentially up to 50%.In recent years a special type of scanning geometry has been proposed. A first prototype of this geometry called CT-DOR(CT with Dual Optimal Reading) has already been built. Despite many drawbacks, resulting images have shown promising potential of dual reading. The approach of gaining two subsets of data has anew been picked up and come to terms with a novel designed CT scanner for breast imaging. The main idea consists of collimating the X-ray beam through a specially designed shielding mask thereby reducing radiation dose without compromising image quality. This is achieved by hexagonally sampled Radon transform and image reconstruction with the especially suitable OPED (orthogonal polynomial expansion on disk) algorithm. This work now presents the development and evaluation of the novel designed breast CT system. Therefore simulated phantom data were obtained to test the performance of the scanning device and compared to a standard 3rd generation scanner. Retaining advantages such as scatter-correction potential and 3D-capability, the proposed CT system yields high resolution images for breast diagnostics in low energy ranges. Assuming similar sample size, it is expected that the novel designed breast CT system in conjunction with OPED outperforms the standard 3rd generation CT system combined with FBP (filtered back projection).

A novel designed x-ray CT scanning geometry is proposed. Composed of a specially designed tungsten collimation mask and a flat panel detector, which is placed inside the mask, this scanning geometry provides high efficient data acquisition allowing dose reduction potential by a factor of two. In recent years a first prototype of the CTDOR geometry (CT with Dual Optimal Reading) has been evaluated. It consisted of a discontinuous ring of detectors fixated on X-Ray absorbing material. The source and an outer detector were mounted on a gantry rotating around the inner static detector and the patient. Despite many drawbacks, resulting images have shown promising potential of dual reading. Based on those results, the present work presents further development and improvement of the recommended scanner geometry. The main idea consists of collimating the X-ray beam through a specially designed shielding mask thereby reducing radiation dose and structuring data without compromising image quality. An especially developed high precision laser-beam cutting process assures an accurate mask crafting with tungsten shielding and window sizes of 300μm. Additionally, simulation data were obtained with Monte Carlo calculations to test the dose reduction potential of the scanning device. Retaining advantages of the CTDOR geometry such as 3D-capability, built-in capacity of scatter correction and radiation structuring, a high-precision manufactured collimation mask of novel designed CT-scanner enables high resolution images for breast-imaging in low energy ranges.

Background There is an opportunity to improve the image quality and lesion detectability in single photon emission computed tomography (SPECT) by choosing an appropriate reconstruction method and optimal parameters for the reconstruction. Purpose To optimize the use of the Flash 3D reconstruction algorithm in terms of equivalent iteration (EI) number (number of subsets times the number of iterations) and to compare with two recently developed reconstruction algorithms ReSPECT and orthogonal polynomial expansion on disc (OPED) for application on 123I-metaiodobenzylguanidine (MIBG)-SPECT. Material and Methods Eleven adult patients underwent SPECT 4 h and 14 patients 24 h after injection of approximately 200 MBq 123I-MIBG using a Siemens Symbia T6 SPECT/CT. Images were reconstructed from raw data using the Flash 3D algorithm at eight different EI numbers. The images were ranked by three experienced nuclear medicine physicians according to their overall impression of the image quality. The obtained optimal images were then compared in one further visual comparison with images reconstructed using the ReSPECT and OPED algorithms. Results The optimal EI number for Flash 3D was determined to be 32 for acquisition 4 h and 24 h after injection. The average rank order (best first) for the different reconstructions for acquisition after 4 h was: Flash 3D32 > ReSPECT > Flash 3D64 > OPED, and after 24 h: Flash 3D16 > ReSPECT > Flash 3D32 > OPED. A fair level of inter-observer agreement concerning optimal EI number and reconstruction algorithm was obtained, which may be explained by the different individual preferences of what is appropriate image quality. Conclusion Using Siemens Symbia T6 SPECT/CT and specified acquisition parameters, Flash 3D32 (4 h) and Flash 3D16 (24 h), followed by ReSPECT, were assessed to be the preferable reconstruction algorithms in visual assessment of 123I-MIBG images.

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In order to decrease the patient's radiation exposure from Computed Tomography, the new CT geometry CTDOR has been invented. It consists of two data sets: A conventional arc or flat panel detector and a mask ring with shieldings on the outside and detectors on the inside separated by windows. Combined with the reconstruction algorithm OPED, it has the theoretical potential to decrease the dose about 50% while providing the same image quality as conventional systems. First steps to evaluate this theory were done with a mask ring demonstrator combined with a conventional C-arm device. Although the quality of the demonstrator is limited, this set-up was supposed to demonstrate how the combination of the two data sets works in principle. Preliminary results from earlier studies, however, provided images of rather poor quality. This work presents better images obtained with an optimized data treatment. We showed that most artifacts are eliminated and that we get sharper images with higher contrast compared to the images reconstructed from the single data sets and compared to the earlier study. Regarding the limitations of the set-up, the resulting images were remarkably good. CTDOR is therefore a promising method, which is worth to perform further studies.

Previously the Orthogonal Polynomial Expansion on the Disk (OPED) algorithm was presented. Further, in prototype experiments in combination with the CT D' or geometry feasibility was demonstrated. In this study we implemented OPED with a clinical Scanner, and evaluated the potential using phantom studies.All studies were acquired on a Siemens Somatom 64 (Erlangen, Germany) scanner, where raw projection data were reconstructed with the conventional FBP reconstruction and the OPED algorithm. OPED allows one to use fan beam geometry directly without any additional procedures such as interpolation or rebinning if using the CT D' or geometry. In particular, OPED describes an approximation of the image function as a sum of polynomials using Chebychev polynomials. For performance evaluation, the Catphan phantom 600 was imaged. OPED Images where reconstructed using C++ and MATLAB (R). We measured uniformity, MTF and CNR for different dose levels and compared these to standard FBP images reconstructions with different filter kernels.The integration and interpretation of the MDCT projection data for the OPED algorithm was accomplished. Reconstruction time is about 6 s on Quad-Core 3 GHz Intel Xeon processor. Typical artifacts are reduced when applying OPED. Using OPED the MTF maintains constant over the whole FOV. Uniformity and CNR are equal compared to FBP.Advantages of OPED were demonstrated by applying the algorithm to projections images from a clinical MDCT scanner. In the future, we see OPED applications for low-dose or limited angle geometries to reduce the radiation dose while improving diagnostic quality of the reconstructed slices.

An angular parameterization of parallel Radon projections referred to in this paper as ψ-parameterization is discussed in relevance to the efficiency of reconstruction from fan data. The fact that the ψ-parameterization coincides with the equiangular fan beam parameterization allows us to develop a simple and efficient approach useful for the reconstruction from fan data. Within this approach parallel projections are approximated by groups of semi-parallel rays. The reconstruction is carried out directly, i.e. without any modification of original data, at the speed which is comparable or even higher than that of the parallel Filtered Back Projection (FBP) algorithm.

This paper discusses the advantages of both geometry of data required for the reconstruction algorithm, orthogonal polynomial expansion on disc (OPED), and polynomial structure of this algorithm. We show that this type of geometry is a result of special parameterisation used within the OPED formalism. The practicability of the OPED data geometry is discussed and it is shown that the data of such geometry can be acquired directly. A method of reducing typical artefacts by using the polynomial structure of the algorithm is summarised as well.