Truncation Artifacts Research Articles

TH‐D‐L100J‐09: CT Truncation Artifact Removal Using Water‐Equivalent Thicknesses Derived From Truncated Projection Data

Purpose: Large patient anatomies and limited imaging field‐of‐view (FOV) lead to truncation of CT projections. Truncation introduces serious artifacts into reconstructed images, including central cupping and bright external rings. FOV may be increased using laterally offset detectors, but this requires advanced imaging hardware and full angular scanning. When linacs equipped with mini‐MLCs are used for megavoltage cone beam CT imaging, truncation is inevitable. We propose a novel method to complete truncated projections based on the observation that the thickness of the patient at all angles may be estimated along the projection rays by calculating water‐equivalent thicknesses (WET). These values are not at all affected by truncation and constitute valuable auxiliary information. Methods: We parameterize a pair of points along each ray that intersects the unknown object boundary. These points are separated by the measured WET value (obtained from projections that have been corrected for scatter and beam‐hardening). We assume, for all large body parts, that the patient outline may be roughly approximated as an ellipse. We use a deterministic optimization algorithm to simultaneously estimate the point positions and ellipse parameters by minimizing the distance between point sets and the ellipse boundary. The ellipse obtained as solution is used to complete the truncated projections before reconstruction. We apply the algorithm to a severely truncated CT dataset of a typical abdomen. Results: The RMS error between non‐truncated and truncated reconstructions is 176%. The correction algorithm reduces this error to 1.0%. Conclusion: Even thought the algorithm assumes an elliptical patient cross‐section, truly impressive increases in quantitative image quality are observed. The presence of pelvic bone in the image does not appreciably bias the ellipse position even though it produces incorrect thickness estimates for some rays. The algorithm incurs low computational burden and is suitable for on‐line clinical work flows. Supported by Siemens.

Spectral Estimation Techniques for DNA Sequence and Microarray Data Analysis

Spectral estimation techniques are widely used in modern signal processing systems. Recently, they have found important applications to the analysis of DNA data. In this paper, we review parametric and non-parametric spectral estimation methods for DNA sequence and microarray data analysis. The discrete Fourier transform (DFT) is the most commonly used technique for spectral analysis of digital signals. It can reveal the gene locations in a DNA sequence. The DFT can also be used to detect repetitive elements in a DNA sequence. The DFT produces the so-called windowing or data truncation artifacts when it is applied to a short data segment. Parametric spectral estimation methods, such as the autoregressive (AR) model, overcome this problem and can be used to obtain a high-resolution spectrum of the input signal. In this paper, we demonstrate the advantages of the AR model for the identification of protein coding regions and the detection of DNA repeats. We also review DFT and AR models and other spectral estimation techniques for the analysis of microarray time series data.

Infrared properties of propagators in Landau-gauge pure Yang-Mills theory at finite temperature

The finite-temperature behavior of gluon and Faddeev-Popov-ghost propagators is investigated for pure $SU(2)$ Yang-Mills theory in Landau gauge. We present nonperturbative results, obtained using lattice simulations and Dyson-Schwinger equations. Possible limitations of these two approaches, such as finite-volume effects and truncation artifacts, are extensively discussed. Both methods suggest a very different temperature dependence for the magnetic sector when compared to the electric one. In particular, a clear thermodynamic transition seems to affect only the electric sector. These results imply, in particular, the confinement of transverse gluons at all temperatures and they can be understood inside the framework of the so-called Gribov-Zwanziger scenario of confinement.

Partial k‐space reconstruction in single‐shot diffusion‐weighted echo‐planar imaging

Partial k-space sampling is frequently used in single-shot diffusion-weighted echo-planar imaging (DW-EPI) to reduce the TE and thereby improve the SNR. However, it increases the sensitivity of the technique to bulk rotational motion, which introduces a phase gradient across the tissue that shifts the echo in k-space. If the echo is displaced into the high spatial frequencies, conventional homodyne reconstruction fails, causing intensity oscillations across the image. Zero-padding, on the other hand, compromises the image resolution and may cause truncation artifacts. We present an adaptive version of the homodyne algorithm that detects the location of the echo in k-space and adjusts the center and width of the homodyne filters accordingly. The adaptive algorithm produces artifact-free images when the echo is shifted into the high positive k-space range, and reduces to the standard homodyne algorithm in the absence of bulk motion.

Parallel acquisition for effective density weighted imaging: PLANED imaging

Density weighted phase-encoding has proven to be a highly efficient method for k-space sampling as it improves the localization properties and increases the signal-to-noise ratio for extended samples at the same time. But either density weighted imaging lengthens the minimum scan time or, if the Nyquist criterion is violated in parts of the sampled k-space, undersampling artefacts occur. Purpose of this work was to combine density weighted imaging and parallel imaging techniques to improve the spatial response function and consequently the signal-to-noise ratio without spoiling image quality by undersampling artefacts. Images were acquired with parallel acquisition for effective density weighted imaging (PLANED imaging) and compared to results sampled with conventional Cartesian phase-encoding with the same spatial resolution and the same number of excitations. Both in vivo and phantom measurements recorded with the PLANED method revealed a considerable enhancement of the signal-to-noise ratio and a remarkable reduction of Gibbs artefacts compared to standard Cartesian imaging. It has been demonstrated that PLANED improves image quality by suppressing truncation artefacts and increasing the SNR without lengthening the measurement time.

Artifacts in body MR imaging: their appearance and how to eliminate them

A wide variety of artifacts can be seen in clinical MR imaging. This review describes the most important and most prevalent of them, including magnetic susceptibility artifacts and motion artifacts, aliasing, chemical-shift, zipper, zebra, central point, and truncation artifacts. Although the elimination of some artifacts may require a service engineer, the radiologist and MR technologist have the responsibility to recognize MR imaging problems. This review shows the typical MR appearance of the described artifacts, explains their physical basis, and shows the way to solve them in daily practice.

MR image reconstruction from partial k-space using singularity function representation

Image reconstruction from partial k-space is an important matter in magnetic resonance imaging (MRI). The previously proposed methods are unable to cope with truncation artifacts without degrading image quality. We present a method that is particularly suitable for reconstructing magnetic resonance (MR) images from partial k-space by reducing substantially truncation artifacts while maintaining the spatial resolution of the image. The proposed method is based on the use of a so-called singularity function representation determined by singular points and singularity degrees. With this model, our strategy consists in restricting the singularity degrees within some dynamic range, beyond which the corresponding singular points are set to zero. The proposed method was evaluated on both simulated and human brain MR data. The results showed that this new strategy has significantly improved the reconstruction quality of partial k-space data.

A generalization of the two-dimensional prolate spheroidal wave function method for nonrectilinear MRI data acquisition methods

The two-dimensional (2-D) prolate spheroidal wave function (2-D PSWF) method was previously introduced as an efficient method for trading off between spatial and temporal resolution in magnetic resonance imaging (MRI), with minimal penalty due to truncation and partial volume effects. In the 2-D PSWF method, the k-space sampling area and a matching 2-D PSWF filter, with optimal signal concentration and minimal truncation artifacts, are determined by the shape and size of a given convex region of interest (ROI). The spatial information in the reduced k-space data is used to calculate the total image intensity over a nonsquare ROI instead of producing a low-resolution image. This method can be used for tracking dynamic signals from non-square ROIs using a reduced k-space sampling area, while achieving minimal signal leakage. However, the previous theory is limited to the case of rectilinear sampling. In order to make the 2-D PSWF method more suitable for dynamic studies, this paper presents a generalized version of the 2-D PSWF theory that can be applied to nonrectilinear data acquisition methods. The method is applied to an fMRI study using a spiral trajectory, which illustrates the methods efficiency at tracking hemodynamic signals with high temporal resolution.

High flow-resolution for mobility estimation in 2D-ENMR of proteins using maximum entropy method (MEM-ENMR)

Multidimensional electrophoretic NMR (nD-ENMR) is a potentially powerful tool for structural characterization of co-existing proteins and protein conformations. By applying a DC electric field pulse, the electrophoretic migration rates of different proteins were detected experimentally in a new dimension of electrophoretic flow. The electrophoretic mobilities were employed to differentiate protein signals. In U-shaped ENMR sample chambers, individual protein components in a solution mixture followed a cosinusoidal electrophoretic interferogram as a function of its unique electrophoretic migration rate. After Fourier transformation in the electrophoretic flow dimension, the protein signals were resolved at different resonant frequencies proportional to their electrophoretic mobilities. Currently, the mobility resolution of the proteins in the electrophoretic flow dimension is limited by severe truncations of the electrophoretic interferograms due to the finite electric field strength available before the onset of heat-induced convection. In this article, we present a successful signal processing method, the Burg’s maximum entropy method (MEM), to analyze the truncated ENMR signals (MEM-ENMR). Significant enhancement in flow resolution was demonstrated using two-dimensional ENMR of two protein samples: a lysozyme solution and a solution mixture of bovine serum albumin (BSA) and ubiquitin. The electrophoretic mobilities of lysozyme, BSA and ubiquitin were measured from the MEM analysis as 7.5 × 10 −5, 1.9 × 10 −4 and 8.7 × 10 −5 cm 2 V −1 s −1, respectively. Results from computer simulations confirmed a complete removal of truncation artifacts in the MEM-ENMR spectra with 3- to 6-fold resolution enhancement.

Automatic estimation of detector radial position for contoured SPECT acquisition using CT images on a SPECT/CT system

An algorithm was developed to estimate noncircular orbit (NCO) single-photon emission computed tomography (SPECT) detector radius on a SPECT/CT imaging system using the CT images, for incorporation into collimator resolution modeling for iterative SPECT reconstruction. Simulated male abdominal (arms up), male head and neck (arms down) and female chest (arms down) anthropomorphic phantom, and ten patient, medium-energy SPECT/CT scans were acquired on a hybrid imaging system. The algorithm simulated inward SPECT detector radial motion and object contour detection at each projection angle, employing the calculated average CT image and a fixed Hounsfield unit (HU) threshold. Calculated radii were compared to the observed true radii, and optimal CT threshold values, corresponding to patient bed and clothing surfaces, were found to be between -970 and -950 HU. The algorithm was constrained by the 45 cm CT field-of-view (FOV), which limited the detected radii to < or = 22.5 cm and led to occasional radius underestimation in the case of object truncation by CT. Two methods incorporating the algorithm were implemented: physical model (PM) and best fit (BF). The PM method computed an offset that produced maximum overlap of calculated and true radii for the phantom scans, and applied that offset as a calculated-to-true radius transformation. For the BF method, the calculated-to-true radius transformation was based upon a linear regression between calculated and true radii. For the PM method, a fixed offset of +2.75 cm provided maximum calculated-to-true radius overlap for the phantom study, which accounted for the camera system's object contour detect sensor surface-to-detector face distance. For the BF method, a linear regression of true versus calculated radius from a reference patient scan was used as a calculated-to-true radius transform. Both methods were applied to ten patient scans. For -970 and -950 HU thresholds, the combined overall average root-mean-square (rms) error in radial position for eight patient scans without truncation were 3.37 cm (12.9%) for PM and 1.99 cm (8.6%) for BF, indicating BF is superior to PM in the absence of truncation. For two patient scans with truncation, the rms error was 3.24 cm (12.2%) for PM and 4.10 cm (18.2%) for BF. The slightly better performance of PM in the case of truncation is anomalous, due to FOV edge truncation artifacts in the CT reconstruction, and thus is suspect. The calculated NCO contour for a patient SPECT/CT scan was used with an iterative reconstruction algorithm that incorporated compensation for system resolution. The resulting image was qualitatively superior to the image obtained by reconstructing the data using the fixed radius stored by the scanner. The result was also superior to the image reconstructed using the iterative algorithm provided with the system, which does not incorporate resolution modeling. These results suggest that, under conditions of no or only mild lateral truncation of the CT scan, the algorithm is capable of providing radius estimates suitable for iterative SPECT reconstruction collimator geometric resolution modeling.

Region of interest reconstruction from truncated data in circular cone-beam CT

The circular scanning trajectory is one of the most widely adopted data-acquisition configurations in computed tomography (CT). The Feldkamp, Davis, Kress (FDK) algorithm and its various modifications have been developed for reconstructing approximately three-dimensional images from circular cone-beam data. When data contain transverse truncations, however, these algorithms may reconstruct images with significant truncation artifacts. It is of practical significance to develop algorithms that can reconstruct region-of-interest (ROI) images from truncated circular cone-beam data that are free of truncation artifacts and that have an accuracy comparable to that obtained from nontruncated cone-beam data. In this work, we have investigated and developed a backprojection-filtration (BPF)-based algorithm for ROI-image reconstruction from circular cone-beam data containing transverse truncations. Furthermore, we have developed a weighted BPF algorithm to exploit "redundant" information in data for improving image quality. In an effort to validate and evaluate the proposed BPF algorithms for circular cone-beam CT, we have performed numerical studies by using both computer-simulation data and experimental data acquired with a radiotherapy cone-beam CT system. Quantitative results in these studies demonstrate that the proposed BPF algorithms for circular cone-beam CT can reconstruct ROI images free of truncation artifacts.

Truncation Artifact on PET/CT: Impact on Measurements of Activity Concentration and Assessment of a Correction Algorithm

Discrepancy between fields of view (FOVs) in a PET/CT scanner causes a truncation artifact when imaging extends beyond the CT FOV. The purposes of this study were to evaluate the impact of this artifact on measurements of 18F-FDG activity concentrations and to assess a truncation correction algorithm. Two phantoms and five patients were used in this study. In the first phantom, three inserts (water, air, bone equivalent) were placed in a water-filled cylinder containing 18F-FDG. In the second phantom study, a chest phantom and a 2-L bottle fitted with a bone insert were used to simulate a patient's torso and arm. Both phantoms were imaged while positioned centrally (baseline) and at the edge of the CT FOV to induce truncation. PET images were reconstructed using attenuation maps from truncated and truncation-corrected CT images. Regions of interest (ROIs) drawn on the inserts, simulated arm, and background water of the baseline truncated and truncation-corrected PET images were compared. In addition, extremity malignancies of five patients truncated on CT images were reconstructed with and without correction and the maximum standard uptake values (SUVs) of the malignancies were compared. Truncation artifact manifests as a rim of high activity concentration at the edge of the truncated CT image with an adjacent low-concentration region peripherally. The correction algorithm minimizes these effects. Phantom studies showed a maximum variation of -5.4% in the truncation-corrected background water image compared with the baseline image. Activity concentration in the water insert was 6.3% higher while that of air and bone inserts was similar to baseline. Extremity malignancies showed a consistent increase in the maximum SUV after truncation correction. Truncation affects measurements of 18F-FDG activity concentrations in PET/CT. A truncation-correction algorithm corrects truncation artifacts with small residual error.

Analysis of a novel offset cone-beam computed mammotomography system geometry for accomodating various breast sizes

We evaluate a newly developed dedicated cone-beam transmission computed mammotomography (CmT) system configuration using an optimized quasi-monochromatic cone beam technique for attenuation correction of SPECT in a planned dual-modality emission and transmission system for pendant, uncompressed breasts. In this study, we perform initial CmT acquisitions using various sized breast phantoms to evaluate an offset cone-beam geometry. This offset geometry provides conjugate projections through a full 360 degree gantry rotation, and thus yields a greatly increased effective field of view, allowing a much wider range of breast sizes to be imaged without truncation in reconstructed images. Using a tungsten X-ray tube and digital flat-panel X-ray detector in a compact geometry, we obtained initial CmT scans without shift and with the offset geometry, using geometrical frequency/resolution phantoms and two different sizes of breast phantoms. Acquired data were reconstructed using an ordered subsets transmission iterative algorithm. Projection images indicate that the larger, 20 cm wide, breast requires use of a half-cone-beam offset scan to eliminate truncation artifacts. Reconstructed image results illustrate elimination of truncation artifacts, and that the novel quasi-monochromatic beam yields reduced beam hardening. The offset geometry CmT system can indeed potentially be used for structural imaging and accurate attenuation correction for the functional dedicated breast SPECT system.

Hybrid integral equation/simulation model for enhancing free energy computations

Integral equation theory is used for extrapolating free energy data from molecular simulations of a reference state with respect to a modification of the interaction potential. The methodology is applied to the correction of artefacts arising from potential shifting and truncation. Corrective contributions for the hydration free energy with respect to the full potential are analysed for the case that both the solute-solvent as well as the solvent-solvent potentials are truncated and modified by a shifted-force term, reaching beyond the range of the dielectric continuum approximation and simple long-range correction expressions. The model systems argon in water and pure water are used as examples for apolar and polar solutes, revealing significant correction contributions even for the short-ranged dispersive interactions and the magnitude of solute-solvent and solvent-solvent components. In comparison with simulation-based extrapolation techniques the integral equation method is shown to be capable of quantitatively predicting truncation artefacts at negligible computational overhead.

Padé methods for reconstruction and feature extraction in magnetic resonance imaging

Methods utilizing Padé approximants are investigated for implementation with magnetic resonance imaging data and are presented both for direct image reconstruction and for feature extraction. Padé approximants are a numerical tool that can be used to accelerate the convergence of a slowly converging sequence by estimating the fully converged sequence values from early data points. Padé approximants can be calculated directly from k-space data by solving a set of linear matrix equations to produce signal values for any desired location in the image domain. This gives an estimate of the fully converged signal intensity at each pixel location in the image, raising the possibility of reconstructing a better estimate of the object from a reduced data set. These methods have been tested on phantom and human data both for image reconstruction and for feature extraction. In image reconstruction, considerable convergence acceleration can be achieved, with steep intensity boundaries reproduced in keeping with higher resolution reconstructions and oscillatory truncation artifact characteristic of Fourier reconstruction removed. The convergence acceleration is variable and there is the possibility of fine detail suppression when insufficient data are included. The use of Padé methods as a tool for feature extraction has shown good agreement with extraction from high-resolution reference data. In this approach the edge information comes intrinsically from Padé reconstruction.

Projection Extension for Region Of Interest Imaging in Cone-Beam CT 1

For 3D X-ray imaging during interventions, changes of the imaged object are often restricted to a small part of the field of view, suggesting region of interest (ROI) imaging by irradiating this area only. In this article, we present a novel method for extension of truncated projections in order to avoid truncation artifacts in C-arm based 3D ROI imaging. The method makes use of prior knowledge by combining forward projections of a previously acquired, nontruncated 3D reference image with the truncated ROI projections. Rigid registration between the two datasets is achieved by using a technique based on local cross-correlation. To account for a gray value mismatch between the two data sets due to, e.g., differing beam quality and different contributions of scattered radiation, a linear gray level transformation is applied to the forward-projected reference data. The performance of different gray value transformation schemes is systematically assessed by means of numerical simulations. For various simulated scenarios, the best performing transformation has been identified, providing practical guidelines for selecting a scheme depending on the origin of the gray-level mismatch. Experiments prove the high performance of the developed method. The presented technique enables almost artifact-free 3D ROI imaging during interventions. This actually allows for repeated scans at low dose and enables intraprocedural imaging of large objects even with a small detector. However, applicability of the method is limited to scenarios where direct access to a reference image, e.g., a prior CT scan, is available.

Cone-beam reconstruction using 1D filtering along the projection of M-lines

In this paper, three exact formulae are derived for cone-beam reconstruction with source positions on a curve or set of curves. For reconstruction at a single point, these formulae all operate by applying a filtration step followed by a backprojection step to cone-beam data. The filtering is performed along a 1D curve which is defined as the intersection of the detector surface with a filtering plane. Two of these formulae allow a flexibility in the choice of the filtering direction. In some cases, this flexibility allows the efficiency of volume reconstruction to be improved. Alternatively, the flexibility can be used to reduce the detector size necessary to avoid truncation artefacts in the reconstruction or to change the noise properties of the reconstruction.

Virtual micro MLC commissioning

The resolution of multileaf collimators (MLCs) is limited by their finite leaf width. A commercial package (HD‐270™) uses 3D couch translation and leaf adjustments to emulate smaller leaf widths. In this paper, we report on the commissioning of this feature using software testing, dial gauge measurements, and film dosimetry. We also identify a variety of limitations: software bugs and truncation artifacts, MLC leaf positioning uncertainties (random variations, systematic gantry dependence and backlash), and uncertainties in couch positioning. These reduce the capabilities of this implementation below that achievable theoretically.PACS numbers: 87.53.Kn, 87.53.Uv, 87.53.Xd

Fast Padé transform for optimal quantification of time signals from magnetic resonance spectroscopy

AbstractThe fast Padé transform (FPT) is both a parametric and a nonparametric estimator that is capable of quantifying the input raw time signals without any fitting. The FPT simultaneously interpolates as well as extrapolates, and this is expected to mitigate truncation artifacts. To assess performance, it is necessary to compare the main features of the FPT with the characteristics of other parametric estimators, as well as with the fast Fourier transform (FFT), which can yield only shape spectra. The FPT can also give the shape of a spectrum, but accomplishes this in two totally different ways, with and without computing the spectral parameters (complex frequencies and amplitudes). A number of other parametric estimators used in signal processing are unable to yield shape spectra without prior extraction of the fundamental frequencies and the corresponding amplitudes. The primary goal of the present study is to assess the accuracy, robustness, and efficiency of the FPT for parametric and nonparametric estimations of experimentally measured time signals from in vivo magnetic resonance spectroscopy (MRS). Robustness and steadiness of the FPT are assessed relative to the FFT by monitoring the convergence rates of these two processors through a systematic and gradual decrease of the truncation level of the full signal length. Accuracy of the FPT is verified by performing error analysis of proven validity, using a gold standard, if available. Alternatively, comparison is made between the two complementary variants of the FPT that converge inside and outside the unit circle. Efficiency of the FPT is checked with respect to the FFT for estimation of the shape of a spectrum, as well as relative to other parametric processors, in the case of quantifications. To establish the accuracy, robustness, and efficiency of the FPT within the outlined multi‐level strategy, we use a time signal encoded via MRS at 4T from the brain of a healthy volunteer. We also assess the overall usefulness of the FPT for signal processing of data acquired from patients, in light of the emerging appreciation that spectroscopy of the tissue metabolites offers a number of vital advantages over the corresponding anatomical imaging in diagnostics. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

A novel algorithm for the reduction of undersampling artefacts in magnetic resonance images

An innovative algorithm is presented which is effective in reducing the truncation artefacts occurring in magnetic resonance images due to missing k-space samples. The algorithm works first by filling the incomplete matrix of coefficients with zeroes and then adjusting, by an iterative process, the missing coefficients by performing a reduction of the undersampling artefacts. Then, this set of coefficients is used as a basis for a superresolution algorithm that estimates the missing coefficients by modeling the data as a linear combination of increasing and decreasing exponential functions using Prony's method. In fact, the Prony's method consists of the interpolation of a given data set with a sum of exponential functions: the MRI signals can be well represented as a sum of exponential functions and the missing data can be extrapolated by this representation. The algorithm has been proven to perform better than either a simple algorithm, which detects and then reduces the undersampling artefacts, or an algorithm that models the measured data with approximation functions. The presented algorithm is quite simple and is applicable both to missing rows (phase-frequency acquisitions) and to radial-missing angle (acquisition from projections) undersampling. Experimental results are reported; comparisons, made between the results obtained using the presented algorithm and the alternative methods described above, clearly demonstrate the superiority of the algorithm.