Segmented multiple plane reconstruction: a novel approximate reconstruction scheme for multi-slice spiral CT

Interesting detector shapes for third generation CT scanners

PURPOSE

To discuss options in designing detector shapes in third generation CT and to quantify potential cost savings for compact third generation CT systems, and to extend the work from two-dimensional fan-beam CT to three-dimensional cone-beam CT for circular, sequential, and spiral scan trajectories.

METHODS

Third generation CT scanners typically comprise detectors which are flat or whose shape is the segment of a cylinder or a sphere that is focused onto the focal spot of the x-ray source. There appear to be two design criteria that favor this choice of detector shape. One is the possibility of performing fan-beam and cone-beam filtered backprojection in the native geometry (without rebinning) and the other criterion could be to enable the early use of focused antiscatter grids. It is less known, however, that other detector shapes may also have these properties. While these designs have been evaluated for 2D CT from a theoretical standpoint more than one decade ago the authors revisit and generalize these considerations, extend them to 3D circular, sequential, and spiral cone-beam CT and propose an optimal design in terms of detector costs while keeping image quality constant. Their considerations and conclusions are based on considering the sampling density of the x-rays, including the effects of finite focal spot and finite detector element size. Proposing image reconstruction algorithms or numerically evaluating the results by reconstructing simulated projection data is not within the scope of this work.

RESULTS

If the detector arc is curved to be nearly concentric with the circle describing the edge of the field of measurement significantly less detector area and detector pixels are required compared to today's third generation CT systems where the detector arc is centered about the focal spot. Combined with a detector that just covers the spiral Tam window cost savings of 60% or more are possible in compact CT systems. In terms of practicability the new designs appear to be nearly as easy to realize as today's third generation systems.

CONCLUSIONS

Compact CT systems, which require the focal spot to be mounted close to the edge of the field of measurement, may significantly benefit from using detector shapes other than the typical equiangular detector that is focused onto the focal spot.

Algorithm for hyperfast cone-beam spiral backprojection

Cone-beam spiral backprojection is computationally highly demanding. At first sight, the backprojection requirements are similar to those of cone-beam backprojection from circular scans such as it is performed in the widely used Feldkamp algorithm. However, there is an additional complication: the illumination of each voxel, i.e. the range of angles the voxel is seen by the X-ray cone is a complex function of the voxel position. The weight function has no analytically closed form and must be numerically determined. Storage of the weights is prohibitive since the amount of memory required equals the number of voxels per spiral rotation times the number of projections a voxel receives contributions and therefore is in the order of 10(9) to 10(11) floating point values for typical spiral scans. We propose a new algorithm that combines the spiral symmetry with the ability of today's 64 bit CPUs to store large amounts of precomputed weights. Using the spiral symmetry in this way allows to exploit data-level parallelism and thereby to achieve a very high level of vectorization. An additional postprocessing step rotates these slices back to normal images. Our new backprojection algorithm achieves up to 24.6 Giga voxel updates per second (GUPS) on our systems that are equipped with two standard Intel X5570 quad core CPUs (Intel Xeon 5500 platform, 2.93 GHz, Intel Corporation). This equals the reconstruction of 410 images per second assuming each slice consists of 512 x 512 pixels, receiving contributions from 512 projections.

Radiation dose reduction in computed tomography: techniques and future perspective

Despite universal consensus that computed tomography (CT) overwhelmingly benefits patients when used for appropriate indications, concerns have been raised regarding the potential risk of cancer induction from CT due to the exponentially increased use of CT in medicine. Keeping radiation dose as low as reasonably achievable, consistent with the diagnostic task, remains the most important strategy for decreasing this potential risk. This article summarizes the general technical strategies that are commonly used for radiation dose management in CT. Dose-management strategies for pediatric CT, cardiac CT, dual-energy CT, CT perfusion and interventional CT are specifically discussed, and future perspectives on CT dose reduction are presented.

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.

Analytic noise-propagation in indirect fan-beam FBP reconstruction

Precise knowledge of the local image noise is an essential ingredient to efficient application of post-processing methods such as wavelet or diffusion filtering to computed tomography (CT) images. The non-stationary, object dependent nature of noise in CT images is a direct result from the noise present in the projection data. Since quantum and electronics noise are the dominating noise sources, comparably simple models can be used for direct noise estimates in the individual projections. In this article, we describe the analytic propagation of these noise estimates through fan-beam filtered backprojection (FBP) reconstruction. Contrary to earlier publications in this field, we include the correlations within the parallel projections resulting from the rebinning, the convolution, and the backprojection processes. The method has been validated against Monte-Carlo results and good accuracy with an average relative error below 3.6% was achieved for arbitrary objects and over the full range of commonly used convolution kernels and field-of-view settings.

Wavelet based noise reduction in CT-images using correlation analysis

The projection data measured in computed tomography (CT) and, consequently, the slices reconstructed from these data are noisy. We present a new wavelet based structure-preserving method for noise reduction in CT-images that can be used in combination with different reconstruction methods. The approach is based on the assumption that data can be decomposed into information and temporally uncorrelated noise. In CT two spatially identical images can be generated by reconstructions from disjoint subsets of projections: using the latest generation dual source CT-scanners one image can be reconstructed from the projections acquired at the first, the other image from the projections acquired at the second detector. For standard CT-scanners the two images can be generated by splitting up the set of projections into even and odd numbered projections. The resulting images show the same information but differ with respect to image noise. The analysis of correlations between the wavelet representations of the input images allows separating information from noise down to a certain signal-to-noise level. Wavelet coefficients with small correlation are suppressed, while those with high correlations are assumed to represent structures and are preserved. The final noise-suppressed image is reconstructed from the averaged and weighted wavelet coefficients of the input images. The proposed method is robust, of low complexity and adapts itself to the noise in the images. The quantitative and qualitative evaluation based on phantom as well as real clinical data showed, that high noise reduction rates of around 40% can be achieved without noticeable loss of image resolution.

Variable pitch reconstruction using John's equation

We present an algorithm to reconstruct helical cone beam computed tomography (CT) data acquired at variable pitch. The algorithm extracts a halfscan segment of projections using an extended version of the advanced single slice rebinning (ASSR) algorithm. ASSR rebins constant pitch cone beam data to fan beam projections that approximately lie on a plane that is tilted to optimally fit the source helix. For variable pitch, the error between the tilted plane chosen by ASSR and the source helix increases, resulting in increased image artifacts. To reduce the artifacts, we choose a reconstruction plane, which is tilted and shifted relative to the source trajectory. We then correct rebinned fan beam data using John's equation to virtually move the source into the tilted and shifted reconstruction plane. Results obtained from simulated phantom images and scanner images demonstrate the applicability of the proposed algorithm.

A rebinned backprojection-filtration algorithm for image reconstruction in helical cone-beam CT

In the last few years, mathematically exact algorithms, including the backprojection-filtration (BPF) algorithm, have been developed for accurate image reconstruction in helical cone-beam CT. The BPF algorithm requires minimum data, and can reconstruct region-of-interest (ROI) images from data containing truncations. However, similar to other existing reconstruction algorithms for helical cone-beam CT, the BPF algorithm involves a backprojection with a spatially varying weighting factor, which is computationally demanding and, more importantly, can lead to undesirable numerical properties in reconstructed images. In this work, we develop a rebinned BPF algorithm in which the backprojection invokes no spatially varying weighting factor for accurate image reconstruction from helical cone-beam projections. This rebinned BPF algorithm is computationally more efficient and numerically more stable than the original BPF algorithm, while it also retains the nice properties of the original BPF algorithm such as minimum data requirement and ROI-image reconstruction from truncated data. We have also performed simulation studies to validate and evaluate the rebinned BPF algorithm.

Hyperfast parallel-beam and cone-beam backprojection using the cell general purpose hardware

Tomographic image reconstruction, such as the reconstruction of computed tomography projection values, of tomosynthesis data, positron emission tomography or SPECT events, and of magnetic resonance imaging data is computationally very demanding. One of the most time-consuming steps is the backprojection. Recently, a novel general purpose architecture optimized for distributed computing became available: the cell broadband engine (CBE). To maximize image reconstruction speed we modified our parallel-beam backprojection algorithm [two dimensional (2D)] and our perspective backprojection algorithm [three dimensional (3D), cone beam for flat-panel detectors] and optimized the code for the CBE. The algorithms are pixel or voxel driven, run with floating point accuracy and use linear (LI) or nearest neighbor (NN) interpolation between detector elements. For the parallel-beam case, 512 projections per half rotation, 1024 detector channels, and an image of size 512(2) was used. The cone-beam backprojection performance was assessed by backprojecting a full circle scan of 512 projections of size 1024(2) into a volume of size 512(3) voxels. The field of view was chosen to completely lie within the field of measurement and the pixel or voxel size was set to correspond to the detector element size projected to the center of rotation divided by square root of 2. Both the PC and the CBE were clocked at 3 GHz. For the parallel backprojection of 512 projections into a 512(2) image, a throughput of 11 fps (LI) and 15 fps (NN) was measured on the PC, whereas the CBE achieved 126 fps (LI) and 165 fps (NN), respectively. The cone-beam backprojection of 512 projections into the 512(3) volume took 3.2 min on the PC and is as fast as 13.6 s on the cell. Thereby, the cell greatly outperforms today's top-notch backprojections based on graphical processing units. Using both CBEs of our dual cell-based blade (Mercury Computer Systems) allows to 2D backproject 330 images/s and one can complete the 3D cone-beam backprojection in 6.8 s.

X-ray spectrum optimization of full-field digital mammography: Simulation and phantom study

In contrast to conventional analog screen-film mammography new flat detectors have a high dynamic range and a linear characteristic curve. Hence, the radiographic technique can be optimized independently of the receptor exposure. It can be exclusively focused on the improvement of the image quality and the reduction of the patient dose. In this paper we measure the image quality by a physical quantity, the signal difference-to-noise ratio (SDNR), and the patient risk by the average glandular dose (AGD). Using these quantities, we compare the following different setups through simulations and phantom studies regarding the detection of microcalcifications and tumors for different breast thicknesses and breast compositions: Monochromatic radiation, three different anode/filter combinations: Molybdenum/molybdenum (Mo/Mo), molybdenum/rhodium (Mo/Rh), and tungsten/rhodium (W/Rh), different filter thicknesses, use of anti-scatter grids, and different tube voltages. For a digital mammography system based on an amorphous selenium detector it turned out that, first, the W/Rh combination is the best choice for all detection tasks studied. Second, monochromatic radiation can further reduce the AGD by a factor of up to 2.3, maintaining the image quality in comparison with a real polychromatic spectrum of an x-ray tube. And, third, the use of an anti-scatter grid is only advantageous for breast thicknesses larger than approximately 5 cm.

Multi–Detector Row CT Coronary Angiography: Influence of Reconstruction Technique and Heart Rate on Image Quality

PURPOSE

To prospectively evaluate to what extent image quality in 16-detector row computed tomographic (CT) coronary angiography is a function of the heart rate and the image reconstruction technique used.

MATERIALS AND METHODS

A total of 70 patients (49 men, 21 women; mean age, 59.1 years +/- 5.8 [standard deviation]) consecutively underwent multi-detector row CT coronary angiography; 49 patients additionally underwent coronary angiography. Image reconstruction was based on both relative and absolute timing. A total of 20 equidistant relative and absolute image reconstructed intervals were assessed by applying a four-step grading scale. Cluster and discrimination analysis, Spearman correlation analysis, and Wilcoxon and chi2 tests were used for statistical analysis. Institutional review board approval and written informed consent were obtained.

RESULTS

Though significantly (P < .001) better image quality was observed for image reconstruction based on absolute timing and in patients with lower heart rates, influence on diagnostic accuracy was not significant. Irrespective of the reconstruction technique used, best image quality was observed in patients with a low heart rate for middiastolic reconstruction intervals (starting points: 61% of R-R interval [range, 40%-75%] and 599.3 msec after R [range, 450-840 msec]) and in patients with a high heart rate for end-systolic or early-diastolic intervals (starting points: 27.3% of R-R interval [range, 10%-45%] and 202.3 msec after R [range, 82-336 msec]). With regard to the vessel section and reconstruction technique, cutoff heart rates of the intervals were 64.0-68.5 beats per minute. Patients with stenoses of more than 50% were identified with 86% sensitivity and specificity, and there was no significant difference between relative and absolute timing (P = .99).

CONCLUSION

In multi-detector row CT coronary angiography, image quality depends on the choice of a suited reconstruction interval. In patients with high heart rates, the best image quality can be obtained with end-systolic and early-diastolic intervals; in patients with low heart rates, the best results are achieved with middiastolic intervals.

The point spread function of spiral CT

Computed tomography (CT) scanners are usually described by their in-plane resolution and slice-sensitivity profile (SSP). Other imaging systems are characterized by their point spread function (PSF). The PSF is an excellent basis for the analysis, design and enhancement of imaging systems. The 3D PSF of CT systems has rarely been considered, and has usually been approximated by a 3D Gaussian. We present mathematical analysis of the PSF of single-slice and multi-slice fan-beam and cone-beam CT, for major reconstruction algorithms. We show that the PSF has a complicated, non-separable 3D shape. It is anisotropic in the xy plane and twisted in the z direction. Furthermore, the PSF is space variant in all three axes. In particular, it rotates as the input impulse function moves in the z direction. The PSF may also have effective discontinuities that can lead to streaking artefacts. Indirect measurements of the PSF can be misleading. We support the theoretical results by direct experimental measurements of the PSF.

Multi-detector row CT systems and image-reconstruction techniques

The introduction in 1998 of multi-detector row computed tomography (CT) by the major CT vendors was a milestone with regard to increased scan speed, improved z-axis spatial resolution, and better utilization of the available x-ray power. In this review, the general technical principles of multi-detector row CT are reviewed as they apply to the established four- and eight-section systems, the most recent 16-section scanners, and future generations of multi-detector row CT systems. Clinical examples are used to demonstrate both the potential and the limitations of the different scanner types. When necessary, standard single-section CT is referred to as a common basis and starting point for further developments. Another focus is the increasingly important topic of patient radiation exposure, successful dose management, and strategies for dose reduction. Finally, the evolutionary steps from traditional single-section spiral image-reconstruction algorithms to the most recent approaches toward multisection spiral reconstruction are traced.

Helical cardiac cone beam CT reconstruction with large area detectors: a simulation study

Retrospectively gated cardiac volume CT imaging has become feasible with the introduction of heart rate adaptive cardiac CT reconstruction algorithms. The development in detector technology and the rapid introduction of multi-row detectors has demanded reconstruction schemes which account for the cone geometry. With the extended cardiac reconstruction (ECR) framework, the idea of approximate helical cone beam CT has been extended to be used with retrospective gating, enabling heart rate adaptive cardiac cone beam reconstruction. In this contribution, the ECR technique is evaluated for systems with an increased number of detector rows, which leads to larger cone angles. A simulation study has been carried out based on a 4D cardiac phantom consisting of a thorax model and a dynamic heart insert. Images have been reconstructed for different detector set-ups. Reconstruction assessment functions have been calculated for the detector set-ups employing different rotation times, relative pitches and heart rates. With the increased volume coverage of large area detector systems, low-pitch scans become feasible without resulting in extensive scan times, inhibiting single breath hold acquisitions. ECR delivers promising image results when being applied to systems with larger cone angles.

Exact and approximate algorithms for helical cone-beam CT

This paper concerns image reconstruction for helical x-ray transmission tomography (CT) with multi-row detectors. We introduce two approximate cone-beam (CB) filtered-backprojection (FBP) algorithms of the Feldkamp type, obtained by extending to three dimensions (3D) two recently proposed exact FBP algorithms for 2D fan-beam reconstruction. The new algorithms are similar to the standard Feldkamp-type FBP for helical CT. In particular, they can reconstruct each transaxial slice from data acquired along an arbitrary segment of helix, thereby efficiently exploiting the available data. In contrast to the standard Feldkamp-type algorithm, however, the redundancy weight is applied after filtering, allowing a more efficient numerical implementation. To partially alleviate the CB artefacts, which increase with increasing values of the helical pitch, a frequency-mixing method is proposed. This method reconstructs the high frequency components of the image using the longest possible segment of helix, whereas the low frequencies are reconstructed using a minimal, short-scan, segment of helix to minimize CB artefacts. The performance of the algorithms is illustrated using simulated data.

General reconstruction theory for multislice X-ray computed tomography with a gantry tilt

This paper discusses image reconstruction with a tilted gantry in multislice computed tomography (CT) with helical (spiral) data acquisition. The reconstruction problem with gantry tilt is shown to be transformable into the problem of reconstructing a virtual object from multislice CT data with no gantry tilt, for which various algorithms exist in the literature. The virtual object is related to the real object by a simple affine transformation that transforms the tilted helical trajectory of the X-ray source into a nontilted helix, and the real object can be computed from the virtual object using one-dimensional interpolation. However, the interpolation may be skipped since the reconstruction of the virtual object on a Cartesian grid provides directly nondistorted images of the real object on slices parallel to the tilted plane of the gantry. The theory is first presented without any specification of the detector geometry, then applied to the curved detector geometry of third-generation CT scanners with the use of Katsevich's formula for example. Results from computer-simulated data of the FORBILD thorax phantom are given in support of the theory.

Multidetector Computed Tomography Technology

By virtue of its speed and isotropic resolution of thin slices, multidetector-row computed tomography (MDCT) offers unique advantages over previous single-detector-row CT, with improved temporal and spatial resolution. This review describes the historical perspective and growth trends of MDCT scanners and highlights the current status and emerging developments in multidetector technology based on presentations at the symposium "Advances in Multidetector CT," under the auspices of the Institute for Advanced Medical Education in Washington, DC.

Extended parallel backprojection for standard three-dimensional and phase-correlated four-dimensional axial and spiral cone-beam CT with arbitrary pitch, arbitrary cone-angle, and 100% dose usage

We have developed a new approximate Feldkamp-type algorithm that we call the extended parallel backprojection (EPBP). Its main features are a phase-weighted backprojection and a voxel-by-voxel 180 degrees normalization. The first feature ensures three-dimensional (3-D) and 4-D capabilities with one and the same algorithm; the second ensures 100% detector usage (each ray is accounted for). The algorithm was evaluated using simulated data of a thorax phantom and a cardiac motion phantom for scanners with up to 256 slices. Axial (circle and sequence) and spiral scan trajectories were investigated. The standard reconstructions (EPBPStd) are of high quality, even for as many as 256 slices. The cardiac reconstructions (EPBPCI) are of high quality as well and show no significant deterioration of objects even far off the center of rotation. Since EPBPCI uses the cardio interpolation (CI) phase weighting the temporal resolution is equivalent to that of the well-established single-slice and multislice cardiac approaches 180 degrees CI, 180 degrees MCI, and ASSRCI, respectively, and lies in the order of 50 to 100 ms for rotation times between 0.4 and 0.5 s. EPBP appears to fulfill all required demands. Especially the phase-correlated EPBP reconstruction of cardiac multiple circle scan data is of high interest, e.g., for dynamic perfusion studies of the heart.

Weighted FBP—a simple approximate 3D FBP algorithm for multislice spiral CT with good dose usage for arbitrary pitch

A new 3D reconstruction scheme, weighted filtered backprojection (WFBP) for multirow spiral CT based on an extension of the two-dimensional SMPR algorithm is described and results are presented. In contrast to other 3D algorithms available, the algorithm makes use of all available data for all pitch values. The algorithm is a FBP algorithm: linear convolution of the parallel data along the row direction followed by a 3D backprojection. Data usage for arbitrary pitch values is maintained through a weighting scheme which takes into account redundant data. If proper row weighting is applied, the image quality is superior to the image quality of the SMPR algorithm.

A quasiexact reconstruction algorithm for helical CT using a 3-Pi acquisition

Recently, an exact reconstruction method for helical CT was published by A. Katsevich. The algorithm is of the filtered backprojection type and is, therefore, computationally efficient. Moreover, during backprojection, only data are used which correspond to an illumination interval of 180 degrees as seen from the object-point. We propose a new reconstruction method, which is applicable to data obtained with a 3-Pi acquisition [IEEE Trans. Med. Imaging 19, 848-863 (2000)]. The method uses the same filter types as the Katsevich algorithm, but the directions and the number of the filter lines are chosen differently. For the derivation of the new algorithm, we analyze the relationship of the Katsevich method and radon inversion. A certain radon plane can intersect with the backprojection interval related to a 3-Pi acquisition either once, three, or five times. In analogy to the definition of quasiexactness introduced by Kudo et al. for a 1-Pi acquisition, we use the term quasiexactness for algorithms on a 3-Pi acquisition, if radon planes with one or three intersections within the backprojection interval are treated correctly. Using the results on the relationship with radon inversion, we can prove that our algorithm is quasiexact in this sense. We use simulation results in order to demonstrate that the algorithm yields excellent image quality.

Image reconstruction and image quality evaluation for a 16-slice CT scanner

We present a theoretical overview and a performance evaluation of a novel approximate reconstruction algorithm for cone-beam spiral CT, the adaptive multiple plane reconstruction (AMPR), which has been introduced by Schaller, Flohr et al. [Proc. SPIE Int. Symp. Med. Imag. 4322, 113-127 (2001)] AMPR has been implemented in a recently introduced 16-slice CT scanner. We present a detailed algorithmic description of AMPR which allows for a free selection of the spiral pitch. We show that dose utilization is better than 90% independent of the pitch. We give an overview on the z-reformation functions chosen to allow for a variable selection of the spiral slice width at arbitrary pitch values. To investigate AMPR image quality we present images of anthropomorphic phantoms and initial patient results. We present measurements of spiral slice sensitivity profiles (SSPs) and measurements of the maximum achievable transverse resolution, both in the isocenter and off-center. We discuss the pitch dependence of image noise measured in a centered 20 cm water phantom. Using the AMPR approach, cone-beam artifacts are considerably reduced for the 16-slice scanner investigated. Image quality in MPRs is independent of the pitch and equivalent to a single-slice CT system at pitch p approximately 1.5. The full width at half-maximum (FWHM) of the spiral SSPs shows only minor variations as a function of the pitch, nominal, and measured values differ by less than 0.2 mm. With 16 x 0.75 mm collimation, the measured FWHM of the smallest reconstructed slice is about 0.9 mm. Using this slice width and overlapping image reconstruction, cylindrical holes with 0.6 mm diameter can be resolved in a z-resolution phantom. Image noise for constant effective mAs is nearly independent of the pitch. Measured and theoretically expected dose utilization are in good agreement. Meanwhile, clinical practice has demonstrated the excellent image quality and the increased diagnostic capability that is obtained with the new generation of multislice CT systems.