Dual-energy computed tomography imaging with megavoltage and kilovoltage X-ray spectra

Purpose

Single-energy computed tomography (CT) often suffers from poor contrast yet remains critical for effective radiotherapy treatment. Modern therapy systems are often equipped with both megavoltage (MV) and kilovoltage (kV) X-ray sources and thus already possess hardware for dual-energy (DE) CT. There is unexplored potential for enhanced image contrast using MV-kV DE-CT in radiotherapy contexts.

Approach

A single-line integral toy model was designed for computing basis material signal-to-noise ratio (SNR) using estimation theory. Five dose-matched spectra (3 kV, 2 MV) and three variables were considered: spectral combination, spectral dose allocation, and object material composition. The single-line model was extended to a simulated CT acquisition of an anthropomorphic phantom with and without a metal implant. Basis material sinograms were computed and synthesized into virtual monoenergetic images (VMIs). MV-kV and kV-kV VMIs were compared with single-energy images.

Results

The 80 kV-140 kV pair typically yielded the best SNRs, but for bone thicknesses > 8    cm , the detunedMV-80 kV pair surpassed it. Peak MV-kV SNR was achieved with ∼ 90 % dose allocated to the MV spectrum. In CT simulations of the pelvis with a steel implant, MV-kV VMIs yielded a higher contrast-to-noise ratio (CNR) than single-energy CT and kV-kV DE-CT. Without steel, the MV-kV VMIs produced higher contrast but lower CNR than single-energy CT.

Conclusions

This work analyzes MV-kV DE-CT imaging and assesses its potential advantages. The technique may be used for metal artifact correction and generation of VMIs with higher native contrast than single-energy CT. Improved denoising is generally necessary for greater CNR without metal.

Special Section Guest Editorial: Computed tomography (CT) at 50 years

Guest editors Patrick La Riviere, Rebecca Fahrig, and Norbert Pelc introduce the JMI Special Section Celebrating X-Ray Computed Tomography at 50.

Single-fluorophore orientation determination with multiview polarized illumination: modeling and microscope design

We investigate the use of polarized illumination in multiview microscopes for determining the orientation of single-molecule fluorescence transition dipoles. First, we relate the orientation of single dipoles to measurable intensities in multiview microscopes and develop an information-theoretic metric-the solid-angle uncertainty-to compare the ability of multiview microscopes to estimate the orientation of single dipoles. Next, we compare a broad class of microscopes using this metric-single- and dual-view microscopes with varying illumination polarization, illumination numerical aperture (NA), detection NA, obliquity, asymmetry, and exposure. We find that multi-view microscopes can measure all dipole orientations, while the orientations measurable with single-view microscopes is halved because of symmetries in the detection process. We also find that choosing a small illumination NA and a large detection NA are good design choices, that multiview microscopes can benefit from oblique illumination and detection, and that asymmetric NA microscopes can benefit from exposure asymmetry.

Improved deconvolution of very weak confocal signals

Deconvolution is typically used to sharpen fluorescence images, but when the signal-to-noise ratio is low, the primary benefit is reduced noise and a smoother appearance of the fluorescent structures. 3D time-lapse (4D) confocal image sets can be improved by deconvolution. However, when the confocal signals are very weak, the popular Huygens deconvolution software erases fluorescent structures that are clearly visible in the raw data. We find that this problem can be avoided by prefiltering the optical sections with a Gaussian blur. Analysis of real and simulated data indicates that the Gaussian blur prefilter preserves meaningful signals while enabling removal of background noise. This approach is very simple, and it allows Huygens to be used with 4D imaging conditions that minimize photodamage.

Improved deconvolution of very weak confocal signals

Deconvolution is typically used to sharpen fluorescence images, but when the signal-to-noise ratio is low, the primary benefit is reduced noise and a smoother appearance of the fluorescent structures. 3D time-lapse (4D) confocal image sets can be improved by deconvolution. However, when the confocal signals are very weak, the popular Huygens deconvolution software erases fluorescent structures that are clearly visible in the raw data. We find that this problem can be avoided by prefiltering the optical sections with a Gaussian blur. Analysis of real and simulated data indicates that the Gaussian blur prefilter preserves meaningful signals while enabling removal of background noise. This approach is very simple, and it allows Huygens to be used with 4D imaging conditions that minimize photodamage.

Variable temporal sampling and tube current modulation for myocardial blood flow estimation from dose-reduced dynamic computed tomography

Quantification of myocardial blood flow (MBF) can aid in the diagnosis and treatment of coronary artery disease. However, there are no widely accepted clinical methods for estimating MBF. Dynamic cardiac perfusion computed tomography (CT) holds the promise of providing a quick and easy method to measure MBF quantitatively. However, the need for repeated scans can potentially result in a high patient radiation dose, limiting the clinical acceptance of this approach. In our previous work, we explored techniques to reduce the patient dose by either uniformly reducing the tube current or by uniformly reducing the number of temporal frames in the dynamic CT sequence. These dose reduction techniques result in noisy time-attenuation curves (TACs), which can give rise to significant errors in MBF estimation. We seek to investigate whether nonuniformly varying the tube current and/or sampling intervals can yield more accurate MBF estimates for a given dose. Specifically, we try to minimize the dose and obtain the most accurate MBF estimate by addressing the following questions: when in the TAC should the CT data be collected and at what tube current(s)? We hypothesize that increasing the sampling rate and/or tube current during the time frames when the myocardial CT number is most sensitive to the flow rate, while reducing them elsewhere, can achieve better estimation accuracy for the same dose. We perform simulations of contrast agent kinetics and CT acquisitions to evaluate the relative MBF estimation performance of several clinically viable variable acquisition methods. We find that variable temporal and tube current sequences can be performed that impart an effective dose of 5.5 mSv and allow for reductions in MBF estimation root-mean-square error on the order of 20% compared to uniform acquisition sequences with comparable or higher radiation doses.

Assessment of vectorial total variation penalties on realistic dual-energy CT data

Vectorial extensions of total variation have recently been developed for regularizing the reconstruction and denoising of multi-channel images, such as those arising in spectral computed tomography. Early studies have focused mainly on simulated, piecewise-constant images whose structure may favor total-variation penalties. In the current manuscript, we apply vectorial total variation to real dual-energy CT data of a whole turkey in order to determine if the same benefits can be observed in more complex images with anatomically realistic textures. We consider the total nuclear variation ([Formula: see text]) as well as another vectorial total variation based on the Frobenius norm ([Formula: see text]) and standard channel-by-channel total variation ([Formula: see text]). We performed a series of 3D TV denoising experiments comparing the three TV variants across a wide range of smoothness parameter settings, optimizing each regularizer according to a very-high-dose 'ground truth' image. Consistent with the simulation studies, we find that both vectorial TV variants achieve a lower error than the channel-by-channel TV and are better able to suppress noise while preserving actual image features. In this real data study, the advantages are subtler than in the previous simulation study, although the [Formula: see text] penalty is found to have clear advantages over either [Formula: see text] or [Formula: see text] when comparing material images formed from linear combinations of the denoised energy images.

Sinogram restoration in computed tomography with an edge-preserving penalty

PURPOSE

With the goal of producing a less computationally intensive alternative to fully iterative penalized-likelihood image reconstruction, our group has explored the use of penalized-likelihood sinogram restoration for transmission tomography. Previously, we have exclusively used a quadratic penalty in our restoration objective function. However, a quadratic penalty does not excel at preserving edges while reducing noise. Here, we derive a restoration update equation for nonquadratic penalties. Additionally, we perform a feasibility study to extend our sinogram restoration method to a helical cone-beam geometry and clinical data.

METHODS

A restoration update equation for nonquadratic penalties is derived using separable parabolic surrogates (SPS). A method for calculating sinogram degradation coefficients for a helical cone-beam geometry is proposed. Using simulated data, sinogram restorations are performed using both a quadratic penalty and the edge-preserving Huber penalty. After sinogram restoration, Fourier-based analytical methods are used to obtain reconstructions, and resolution-noise trade-offs are investigated. For the fan-beam geometry, a comparison is made to image-domain SPS reconstruction using the Huber penalty. The effects of varying object size and contrast are also investigated. For the helical cone-beam geometry, we investigate the effect of helical pitch (axial movement/rotation). Huber-penalty sinogram restoration is performed on 3D clinical data, and the reconstructed images are compared to those generated with no restoration.

RESULTS

We find that by applying the edge-preserving Huber penalty to our sinogram restoration methods, the reconstructed image has a better resolution-noise relationship than an image produced using a quadratic penalty in the sinogram restoration. However, we find that this relatively straightforward approach to edge preservation in the sinogram domain is affected by the physical size of imaged objects in addition to the contrast across the edge. This presents some disadvantages of this method relative to image-domain edge-preserving methods, although the computational burden of the sinogram-domain approach is much lower. For a helical cone-beam geometry, we found applying sinogram restoration in 3D was reasonable and that pitch did not make a significant difference in the general effect of sinogram restoration. The application of Huber-penalty sinogram restoration to clinical data resulted in a reconstruction with less noise while retaining resolution.

CONCLUSIONS

Sinogram restoration with the Huber penalty is able to provide better resolution-noise performance than restoration with a quadratic penalty. Additionally, sinogram restoration with the Huber penalty is feasible for helical cone-beam CT and can be applied to clinical data.

Material identification in x-ray microscopy and micro CT using multi-layer, multi-color scintillation detectors

We demonstrate that a dual-layer, dual-color scintillator construct for microscopic CT, originally proposed to increase sensitivity in synchrotron imaging, can also be used to perform material quantification and classification when coupled with polychromatic illumination. We consider two different approaches to data handling: (1) a data-domain material decomposition whose estimation performance can be characterized by the Cramer-Rao lower bound formalism but which requires careful calibration and (2) an image-domain material classification approach that is more robust to calibration errors. The data-domain analysis indicates that useful levels of SNR (>5) could be achieved in one second or less at typical bending magnet fluxes for relatively large amounts of contrast (several mm path length, such as in a fluid flow experiment) and at typical undulator fluxes for small amount of contrast (tens of microns path length, such as an angiography experiment). The tools introduced could of course be used to study and optimize parameters for a wider range of potential applications. The image domain approach was analyzed in terms of its ability to distinguish different elemental stains by characterizing the angle between the lines traced out in a two-dimensional space of effective attenuation coefficient in the front and back layer images. This approach was implemented at a synchrotron and the results were consistent with simulation predictions.

Joint reconstruction of multi-channel, spectral CT data via constrained total nuclear variation minimization

We explore the use of the recently proposed 'total nuclear variation' (TVN) as a regularizer for reconstructing multi-channel, spectral CT images. This convex penalty is a natural extension of the total variation (TV) to vector-valued images and has the advantage of encouraging common edge locations and a shared gradient direction among image channels. We show how it can be incorporated into a general, data-constrained reconstruction framework and derive update equations based on the first-order, primal-dual algorithm of Chambolle and Pock. Early simulation studies based on the numerical XCAT phantom indicate that the inter-channel coupling introduced by the TVN leads to better preservation of image features at high levels of regularization, compared to independent, channel-by-channel TV reconstructions.

Sinogram smoothing techniques for myocardial blood flow estimation from dose-reduced dynamic computed tomography

Dynamic contrast-enhanced computed tomography (CT) could provide an accurate and widely available technique for myocardial blood flow (MBF) estimation to aid in the diagnosis and treatment of coronary artery disease. However, one of its primary limitations is the radiation dose imparted to the patient. We are exploring techniques to reduce the patient dose by either reducing the tube current or by reducing the number of temporal frames in the dynamic CT sequence. Both of these dose reduction techniques result in noisy data. In order to extract the MBF information from the noisy acquisitions, we have explored several data-domain smoothing techniques. In this work, we investigate two specific smoothing techniques: the sinogram restoration technique in both the spatial and temporal domains and the use of the Karhunen-Loeve (KL) transform to provide temporal smoothing in the sinogram domain. The KL transform smoothing technique has been previously applied to dynamic image sequences in positron emission tomography. We apply a quantitative two-compartment blood flow model to estimate MBF from the time-attenuation curves and determine which smoothing method provides the most accurate MBF estimates in a series of simulations of different dose levels, dynamic contrast-enhanced cardiac CT acquisitions. As measured by root mean square percentage error (% RMSE) in MBF estimates, sinogram smoothing generally provides the best MBF estimates except for the cases of the lowest simulated dose levels (tube current = 25 mAs, 2 or 3 s temporal spacing), where the KL transform method provides the best MBF estimates. The KL transform technique provides improved MBF estimates compared to conventional processing only at very low doses (<7 mSv). Results suggest that the proposed smoothing techniques could provide high fidelity MBF information and allow for substantial radiation dose savings.

X-ray tomography system to investigate granular materials during mechanical loading

We integrate a small and portable medical x-ray device with mechanical testing equipment to enable in situ, non-invasive measurements of a granular material's response to mechanical loading. We employ an orthopedic C-arm as the x-ray source and detector to image samples mounted in the materials tester. We discuss the design of a custom rotation stage, which allows for sample rotation and tomographic reconstruction under applied compressive stress. We then discuss the calibration of the system for 3D computed tomography, as well as the subsequent image reconstruction process. Using this system to reconstruct packings of 3D-printed particles, we resolve packing features with 0.52 mm resolution in a (60 mm)(3) field of view. By analyzing the performance bounds of the system, we demonstrate that the reconstructions exhibit only moderate noise.

Comparison of photoacoustic image reconstruction algorithms using the channelized Hotelling observer

We demonstrate the use of task-based image-quality metrics to compare various photoacoustic image-reconstruction algorithms, including a method based on the pseudoinverse of the system matrix, simple backprojection, filtered backprojection, and a method based on the Fourier transform. We use a three-dimensional forward model with a linear transducer array to simulate a photoacoustic imaging system. The reconstructed images correspond with two-dimensional slices of the object and are 128×128 pixels. In order to compare the algorithms, we use channelized Hotelling observers that predict the detection ability of human observers. We use two sets of channels: constant Q and difference of Gaussian spatial frequency channels. We look at three tasks, identification of a point source in a uniform background, identification of a 0.5-mm cube in a uniform background, and identification of a point source in a lumpy background. For the lumpy background task, which is the most realistic of the tasks, the method based on the pseudoinverse performs best according to both sets of channels.

Photoacoustic image reconstruction in an attenuating medium using singular-value decomposition

Attenuation effects can be significant in photoacoustic tomography since the generated pressure signals are broadband, and ignoring them may lead to image artifacts and blurring. La Rivière et al. [Opt. Lett. 31(6), pp. 781-783, (2006)] had previously derived a method for modeling the attenuation effect and correcting for it in the image reconstruction. This was done by relating the ideal, unattenuated pressure signals to the attenuated pressure signals via an integral operator. We derive an integral operator relating the attenuated pressure signals to the absorbed optical energy for a planar measurement geometry. The matrix operator relating the two quantities is a function of the temporal frequency, attenuation coefficient and the two-dimensional spatial frequency. We perform singular-value decomposition (SVD) of this integral operator to study the problem further. We find that the smallest singular values correspond to wavelet-like eigenvectors in which most of the energy is concentrated at times corresponding to greater depths in tissue. This allows us to characterize the ill-posedness of recovering the absorbed optical energy distribution at different depths in an attenuating medium. This integral equation can be inverted using standard SVD methods, and the initial pressure distribution can be recovered. We conduct simulations and derive an algorithm for image reconstruction using SVD for a planar measurement geometry. We also study the noise and resolution properties of this image-reconstruction method.

Comparison of sinogram- and image-domain penalized-likelihood image reconstruction estimators

PURPOSE

In recent years, the authors and others have been exploring the use of penalized-likelihood sinogram-domain smoothing and restoration approaches for emission and transmission tomography. The motivation for this strategy was initially pragmatic: to provide a more computationally feasible alternative to fully iterative penalized-likelihood image reconstruction involving expensive backprojections and reprojections, while still obtaining some of the benefits of the statistical modeling employed in penalized-likelihood approaches. In this work, the authors seek to compare the two approaches in greater detail.

METHODS

The sinogram-domain strategy entails estimating the "ideal" line integrals needed for reconstruction of an activity or attenuation distribution from the set of noisy, potentially degraded tomographic measurements by maximizing a penalized-likelihood objective function. The objective function models the data statistics as well as any degradation that can be represented in the sinogram domain. The estimated line integrals can then be input to analytic reconstruction algorithms such as filtered backprojection (FBP). The authors compare this to fully iterative approaches maximizing similar objective functions.

RESULTS

The authors present mathematical analyses based on so-called equivalent optimization problems that establish that the approaches can be made precisely equivalent under certain restrictive conditions. More significantly, by use of resolution-variance tradeoff studies, the authors show that they can yield very similar performance under more relaxed, realistic conditions.

CONCLUSIONS

The sinogram- and image-domain approaches are equivalent under certain restrictive conditions and can perform very similarly under more relaxed conditions. The match is particularly good for fully sampled, high-resolution CT geometries. One limitation of the sinogram-domain approach relative to the image-domain approach is the difficulty of imposing additional constraints, such as image non-negativity.

Comparison of intensity-modulated continuous-wave lasers with a chirped modulation frequency to pulsed lasers for photoacoustic imaging applications

Using a Green's function solution to the photoacoustic wave equation, we compare intensity-modulated continuous-wave (CW) lasers with a chirped modulation frequency to pulsed lasers for photoacoustic imaging applications. Assuming the same transducer is used in both cases, we show that the axial resolution is identical and is determined by the transducer and material properties of the object. We derive a simple formula relating the signal-to-noise ratios (SNRs) of the two imaging systems that only depends on the fluence of each pulse and the time-bandwidth product of the chirp pulse. We also compare the SNR of the two systems assuming the fluence is limited by the American National Standards Institute (ANSI) laser safety guidelines for skin. We find that the SNR is about 20 dB to 30 dB larger for pulsed laser systems for reasonable values of the parameters. However, CW diode lasers have the advantage of being compact and relatively inexpensive, which may outweigh the lower SNR in many applications.

Image reconstruction in photoacoustic tomography with variable speed of sound using a higher-order geometrical acoustics approximation

Previous research correcting for variable speed of sound in photoacoustic tomography (PAT) based on a generalized radon transform (GRT) model assumes first-order geometrical acoustics (GA) approximation. In the GRT model, the pressure is related to the optical absorption, in an acoustically inhomogeneous medium, through integration over nonspherical isochronous surfaces. Previous research based on the GRT model assumes that the path taken by acoustic rays is linear and neglects amplitude perturbations to the measured pressure. We have derived a higher-order GA expression that takes into account the first-order effect in the amplitude of the measured signal and higher-order perturbation to the travel times. The higher-order perturbation to travel time incorporates the effect of ray bending. Incorrect travel times can lead to image distortion and blurring. These corrections are expected to impact image quality and quantitative PAT. We have previously shown that travel-time corrections in 2-D suggest that perceivable differences in the isochronous surfaces can be seen when the second-order travel-time perturbations are taken into account with a 10% speed-of-sound variation. In this work, we develop iterative image reconstruction algorithms that incorporate this higher-order GA approximation assuming that the speed of sound map is known. We evaluate the effect of higher-order GA approximation on image quality and accuracy.

Implementation and comparison of reconstruction algorithms for two-dimensional optoacoustic tomography using a linear array

Our goal is to compare and contrast various image reconstruction algorithms for optoacoustic tomography (OAT) assuming a finite linear aperture of the kind that arises when using a linear-array transducer. Because such transducers generally have tall, narrow elements, they are essentially insensitive to out-of-plane acoustic waves, and the usually 3-D OAT problem reduces to a 2-D problem. Algorithms developed for the 3-D problem may not perform optimally in 2-D. We have implemented and evaluated a number of previously described OAT algorithms, including an exact (in 3-D) Fourier-based algorithm and a synthetic-aperture-based algorithm. We have also implemented a 2-D algorithm developed by Norton for reflection mode tomography that has not, to the best of our knowledge, been applied to OAT before. Our simulation studies of resolution, contrast, noise properties, and signal detectability measures suggest that Norton's approach-based algorithm has the best contrast, resolution, and signal detectability.

Correction for resolution nonuniformities caused by anode angulation in computed tomography

Most X-ray tubes comprise a rotating anode that is bombarded with electrons to produce X-rays. A substantial amount of heat is generated, and to increase the area of the anode exposed to the electrons, without increasing the apparent size of the focal spot, the focal track of the anode is generally beveled with a very shallow angle (typically 5 degrees-7 degrees in a computed tomography (CT) tube). Due to the line focus principle, this allows a fairly large area of the focal track to be exposed to electrons while retaining a fairly small effective projected focal spot. One side effect of anode angulation is that the focal spot appears different from different positions in the detector array; the effective focal spot size at a constant distance from the tube will be larger for a peripheral detector channel than for a central one. These differences in the effective size of the focal spot across the field-of-view lead to worse resolution in the periphery than in the center of reconstructed images. In this work we describe a method for achieving more uniform resolution in fanbeam CT images by correcting for these focal spot angulation effects. We do so by modeling the effects as a series of local blurrings in the space of transmitted CT intensities and determining the effective coefficients of the corresponding discrete convolutions. The effect of these blurrings can then be compensated for in the sinogram domain through the use of a penalized-likelihood sinogram restoration model we have recently developed.

Monotonic penalized-likelihood image reconstruction for X-ray fluorescence computed tomography

In this paper, we derive a monotonic penalized-likelihood algorithm for image reconstruction in X-ray fluorescence computed tomography (XFCT) when the attenuation maps at the energies of the fluorescence X-rays are unknown. In XFCT, a sample is irradiated with pencil beams of monochromatic synchrotron radiation that stimulate the emission of fluorescence X-rays from atoms of elements whose K- or L-edges lie below the energy of the stimulating beam. Scanning and rotating the object through the beam allows for acquisition of a tomographic dataset that can be used to reconstruct images of the distribution of the elements in question. XFCT is a stimulated emission tomography modality, and it is thus necessary to correct for attenuation of the incident and fluorescence photons. The attenuation map is, however, generally known only at the stimulating beam energy and not at the energies of the various fluorescence X-rays of interest. We have developed a penalized-likelihood image reconstruction strategy for this problem. The approach alternates between updating the distribution of a given element and updating the attenuation map for that element's fluorescence X-rays. The approach is guaranteed to increase the penalized likelihood at each iteration. Because the joint objective function is not necessarily concave, the approach may drive the solution to a local maximum. To encourage the algorithm to seek out a reasonable local maximum, we include in the objective function a prior that encourages a relationship, based on physical considerations, between the fluorescence attenuation map and the distribution of the element being reconstructed.

Penalized-likelihood sinogram restoration for computed tomography

We formulate computed tomography (CT) sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy, degraded measurements. CT measurement data are degraded by a number of factors-including beam hardening and off-focal radiation-that produce artifacts in reconstructed images unless properly corrected. Currently, such effects are addressed by a sequence of sinogram-preprocessing steps, including deconvolution corrections for off-focal radiation, that have the potential to amplify noise. Noise itself is generally mitigated through apodization of the reconstruction kernel, which effectively ignores the measurement statistics, although in high-noise situations adaptive filtering methods that loosely model data statistics are sometimes applied. As an alternative, we present a general imaging model relating the degraded measurements to the sinogram of ideal line integrals and propose to estimate these line integrals by iteratively optimizing a statistically based objective function. We consider three different strategies for estimating the set of ideal line integrals, one based on direct estimation of ideal "monochromatic" line integrals that have been corrected for single-material beam hardening, one based on estimation of ideal "polychromatic" line integrals that can be readily mapped to monochromatic line integrals, and one based on estimation of ideal transmitted intensities, from which ideal, monochromatic line integrals can be readily estimated. The first two approaches involve maximization of a penalized Poisson-likelihood objective function while the third involves minimization of a quadratic penalized weighted least squares (PWLS) objective applied in the transmitted intensity domain. We find that at low exposure levels typical of those being considered for screening CT, the Poisson-likelihood based approaches outperform the PWLS objective as well as a standard approach based on adaptive filtering followed by deconvolution. At higher exposure levels, the approaches all perform similarly.

Image reconstruction in optoacoustic tomography for dispersive acoustic media

Conventional image reconstruction methods for optoacoustic tomography (OAT) assume an idealized, non-dispersive acoustic medium. However, the linear attenuation coefficient and the phase velocity of acoustic waves propagating in soft tissue depend on temporal frequency and satisfy a known dispersion law. These frequency-dependent effects are incorporated into an optoacoustic wave equation, and a corresponding reconstruction method for OAT is developed. The improvement in image fidelity that can be achieved over conventional reconstruction methods is demonstrated by use of computer-simulation studies.

Penalized-likelihood sinogram smoothing for low-dose CT

We have developed a sinogram smoothing approach for low-dose computed tomography (CT) that seeks to estimate the line integrals needed for reconstruction from the noisy measurements by maximizing a penalized-likelihood objective function. The maximization is performed by an algorithm derived by use of the separable paraboloidal surrogates framework. The approach overcomes some of the computational limitations of a previously proposed spline-based penalized-likelihood sinogram smoothing approach, and it is found to yield better resolution-variance tradeoffs than this spline-based approach as well an existing adaptive filtering approach. Such sinogram smoothing approaches could be valuable when applied to the low-dose data acquired in CT screening exams, such as those being considered for lung-nodule detection.

Reduction of noise-induced streak artifacts in X-ray computed tomography through spline-based penalized-likelihood sinogram smoothing

We present a statistically principled sinogram smoothing approach for X-ray computed tomography (CT) with the intent of reducing noise-induced streak artifacts. These artifacts arise in CT when some subset of the transmission measurements capture relatively few photons because of high attenuation along the measurement lines. Attempts to reduce these artifacts have focused on the use of adaptive filters that strive to tailor the degree of smoothing to the local noise levels in the measurements. While these approaches involve loose consideration of the measurement statistics to determine smoothing levels, they do not explicitly model the statistical distributions of the measurement data. In this paper, we present an explicitly statistical approach to sinogram smoothing in the presence of photon-starved measurements. It is an extension of a nonparametric sinogram smoothing approach using penalized Poisson-likelihood functions that we have previously developed for emission tomography. Because the approach explicitly models the data statistics, it is naturally adaptive--it will smooth more variable measurements more heavily than it does less variable measurements. We find that it significantly reduces streak artifacts and noise levels without comprising image resolution.

Approximate analytic reconstruction in x-ray fluorescence computed tomography

X-ray fluorescence computed tomography (XFCT) is an emerging imaging modality that allows for the reconstruction of the distribution of nonradioactive elements within a sample from measurements of fluorescence x-rays produced by irradiation of the sample with monochromatic synchrotron radiation. XFCT is not a transmission tomography modality, but rather a stimulated emission tomography modality and thus correction for attenuation of the incident and fluorescence photons is essential if accurate images are to be obtained. In this work, we develop and characterize an approximate analytic approach to image reconstruction with attenuation correction in XFCT that is applicable when the incident beam attenuation is uniform and when a factor involving fluorescence attenuation and solid angle effects satisfies a certain approximation. When these conditions hold, we demonstrate that the XFCT imaging equation reduces to the exponential Radon transform, which can be readily inverted. The necessary approximation worsens as the total fluorescence attenuation in the sample grows, but the approach is found to be relatively robust as the approximation breaks down. In a long-axis, small solid angle geometry the proposed approach performs comparably to a previously proposed, more computationally expensive approximate method across a range of attenuation levels. In a short-axis, large solid angle geometry, the proposed approach is found to outperform this previous method.

Sampling and aliasing consequences of quarter-detector offset use in helical CT

In this paper, the sampling and aliasing consequences of employing a quarter-detector-offset (QDO) in helical computed tomography (CT) are analyzed. QDO is often used in conventional CT to reduce in-plane aliasing by eliminating data redundancies to improve radial sampling. In helical CT, these same redundancies are exploited to improve longitudinal sampling and so it might seem ill-advised to employ QDO. The relative merit of the two geometries for helical CT is studied by conducting a multidimensional sampling analysis of projection-space sampling as well as a Fourier crosstalk analysis of crosstalk among the object's Fourier basis components. Both a standard fanbeam helical CT geometry and a hypothetical parallel-beam CT geometry, which helps illuminate the more complicated fanbeam results, are analyzed. Using the sampling analysis, it was found that the use of QDO leads to very different spectral tiling than arise when not using QDO. However, due to the shape of the essential support of the projection data spectra that arises in practice, both configurations lead to very similar or identical amounts of spectral overlap. This perspective also predicts the spatially variant longitudinal aliasing that has been observed in helical CT. The crosstalk results were consistent with those of the multidimensional sampling analysis. Thus, from the standpoint of aliasing and crosstalk, no compelling difference is found between the two geometries.

Automated detection of lung nodules in CT scans: effect of image reconstruction algorithm

We have investigated the effect of computed tomography (CT) image reconstruction algorithm on the performance of our automated lung nodule detection method. Commercial CT scanners offer a choice of several algorithms for the reconstruction of projection data into transaxial images. Different algorithms produce images with substantially different properties that are apparent not only quantitatively, but also through visual assessment. During some clinical thoracic CT examinations, patient scans are reconstructed with multiple reconstruction algorithms. Thirty-eight such cases were collected to form two databases: one with patient projection data reconstructed with the "standard" reconstruction algorithm and the other with the same patient projection data reconstructed with the "lung" reconstruction algorithm. The automated nodule detection method was applied to both databases. This method is based on gray-level-thresholding techniques to segment the lung regions from each CT section to create a segmented lung volume. Further gray-level-thresholding techniques are applied within the segmented lung volume to identify a set of lung nodule candidates. Rule-based and linear discriminant classifiers are used to differentiate between lung nodule candidates that correspond to actual nodules and those that correspond to non-nodules. The automated method that was applied to both databases was exactly the same, except that the classifiers were calibrated separately for each database. For comparison, the classifier then was trained on one database and tested independently on the other database. When applied to the databases in this manner, the automated method demonstrated overall a similar level of performance, indicating an encouraging degree of robustness.

Longitudinal aliasing in multislice helical computed tomography: sampling and cone-beam effects

In this study, we examine longitudinal aliasing properties in multislice helical computed tomography (CT) volumes reconstructed under the multiple parallel fanbeam approximation by use of a 180LI-type algorithm. We focus on the differences between the multislice case and the single-slice case, which has been studied previously. Specifically, we examine longitudinal aliasing properties in four-slice scanners for helical pitches 3 and 6, which are sometimes called "preferred" in four-slice helical CT, because it is believed that the effective longitudinal sampling intervals at these pitches are equivalent to those in single-slice helical CT operating at pitches 1 and 2, respectively. While these equivalences have been supported by comparative studies of slice-sensitivity profiles in single- and multislice helical CT, artifacts have been observed in pitch-3 and pitch-6 multislice images that were not evident in their purported single-slice counterparts. We attribute these differences to aliasing arising in the multislice reconstructions that is not present in the single-slice counterparts. We find that the aliasing has two principal origins: sampling effects similar to those in the single-slice case and cone-beam effects. The difference between the multislice, pitch-3 and single-slice, pitch-1 results is attributed to the small cone angle in multislice helical CT, which introduces inconsistencies among the measurements of different detector rows. The difference between multislice, pitch-6 and single-slice, pitch-2 results is attributed to a combination of the cone angle and genuine differences in sampling patterns. It is argued, however, that the lack of strict equivalence with single-slice counterparts does not necessarily undermine the claim that pitches 3 and 6 are "preferred" relative to other pitches in multislice helical CT.

Pitch dependence of longitudinal sampling and aliasing effects in multi-slice helical computed tomography (CT)

In this work, we investigate longitudinal sampling and aliasing effects in multi-slice helical CT. We demonstrate that longitudinal aliasing can be a significant, complicated, and potentially detrimental effect in multi-slice helical CT reconstructions. Multi-slice helical CT scans are generally undersampled longitudinally for all pitches of clinical interest, and the resulting aliasing effects are spatially variant. As in the single-slice case, aliasing is shown to be negligible at the isocentre for circularly symmetric objects due to a fortuitous aliasing cancellation phenomenon. However, away from the isocentre, aliasing effects can be significant, spatially variant, and highly pitch dependent. This implies that measures more sophisticated than isocentre slice sensitivity profiles are needed to characterize longitudinal properties of multi-slice helical CT systems. Such measures are particularly important in assessing the question of whether there are preferred pitches in helical CT. Previous analyses have generally focused only on isocentre sampling patterns, and our more global analysis leads to somewhat different conclusions than have been reached before, suggesting that pitches 3, 4, 5, and 6 are favourable, and that half-integer pitches are somewhat suboptimal.

Pitch dependence of longitudinal sampling and aliasing effects in multi-slice helical computed tomography (CT)

In this work, we investigate longitudinal sampling and aliasing effects in multi-slice helical CT. We demonstrate that longitudinal aliasing can be a significant, complicated, and potentially detrimental effect in multi-slice helical CT reconstructions. Multi-slice helical CT scans are generally undersampled longitudinally for all pitches of clinical interest, and the resulting aliasing effects are spatially variant. As in the single-slice case, aliasing is shown to be negligible at the isocentre for circularly symmetric objects due to a fortuitous aliasing cancellation phenomenon. However, away from the isocentre, aliasing effects can be significant, spatially variant, and highly pitch dependent. This implies that measures more sophisticated than isocentre slice sensitivity profiles are needed to characterize longitudinal properties of multi-slice helical CT systems. Such measures are particularly important in assessing the question of whether there are preferred pitches in helical CT. Previous analyses have generally focused only on isocentre sampling patterns, and our more global analysis leads to somewhat different conclusions than have been reached before, suggesting that pitches 3, 4, 5, and 6 are favourable, and that half-integer pitches are somewhat suboptimal.

Anti-aliasing weighting functions for single-slice helical CT

Spatially variant longitudinal aliasing plagues most volumes reconstructed from single-slice helical computed tomography data, and its presence can degrade resolution and distort image structures. We have recently developed a Fourier-based approach to longitudinal interpolation in helical computed tomography that can, for scans performed at pitch 1 or lower, essentially eliminate this longitudinal aliasing by exploiting a generalization of the Whittaker-Shannon sampling theorem whose conditions are satisfied by the interlaced pairs of direct and complementary longitudinal samples. However, the algorithm is computationally intensive and cannot be pipelined. In this paper, we address this shortcoming by deriving two spatial-domain, projection-data weighting functions that approximate the application of the Fourier-based approach, and preserve its aliasing suppression properties to some degree, while allowing for a pipelined implementation. The first approach, which we call simply 180AA, for anti-aliasing, is a direct spatial-domain approximation of the 180FT approach. The second approach, which we call 180BSP, is based on an approximate generalized interpolation approach making use of B-splines. Studies of aliasing and resolution properties in reconstructions from simulated data indicate that while the 180AA and 180BSP approaches do not perfectly replicate the favorable aliasing suppression and resolution properties of the 180FT approach, they do represent an improvement over the clinically standard 180LI approach on these fronts.

Favorable noise uniformity properties of Fourier-based interpolation and reconstruction approaches in single-slice helical computed tomography

Volumes reconstructed by standard methods from single-slice helical computed tomography (CT) data have been shown to have noise levels that are highly nonuniform relative to those in conventional CT. These noise nonuniformities can affect low-contrast object detectability and have also been identified as the cause of the zebra artifacts that plague maximum intensity projection (MIP) images of such volumes. While these spatially variant noise levels have their root in the peculiarities of the helical scan geometry, there is also a strong dependence on the interpolation and reconstruction algorithms employed. In this paper, we seek to develop image reconstruction strategies that eliminate or reduce, at its source, the nonuniformity of noise levels in helical CT relative to that in conventional CT. We pursue two approaches, independently and in concert. We argue, and verify, that Fourier-based longitudinal interpolation approaches lead to more uniform noise ratios than do the standard 360LI and 180LI approaches. We also demonstrate that a Fourier-based fan-to-parallel rebinning algorithm, used as an alternative to fanbeam filtered backprojection for slice reconstruction, also leads to more uniform noise ratios, even when making use of the 180LI and 360LI interpolation approaches.