Modeling the axial extension of a transmission line source within iterative reconstruction via multiple transmission sources

Modelling the physics in the iterative reconstruction for transmission computed tomography

There is an increasing interest in iterative reconstruction (IR) as a key tool to improve quality and increase applicability of x-ray CT imaging. IR has the ability to significantly reduce patient dose; it provides the flexibility to reconstruct images from arbitrary x-ray system geometries and allows one to include detailed models of photon transport and detection physics to accurately correct for a wide variety of image degrading effects. This paper reviews discretization issues and modelling of finite spatial resolution, Compton scatter in the scanned object, data noise and the energy spectrum. The widespread implementation of IR with a highly accurate model-based correction, however, still requires significant effort. In addition, new hardware will provide new opportunities and challenges to improve CT with new modelling.

Modelling the physics in the iterative reconstruction for transmission computed tomography

There is an increasing interest in iterative reconstruction (IR) as a key tool to improve quality and increase applicability of x-ray CT imaging. IR has the ability to significantly reduce patient dose; it provides the flexibility to reconstruct images from arbitrary x-ray system geometries and allows one to include detailed models of photon transport and detection physics to accurately correct for a wide variety of image degrading effects. This paper reviews discretization issues and modelling of finite spatial resolution, Compton scatter in the scanned object, data noise and the energy spectrum. The widespread implementation of IR with a highly accurate model-based correction, however, still requires significant effort. In addition, new hardware will provide new opportunities and challenges to improve CT with new modelling.

Direction-dependent localization errors in SPECT images

PURPOSE

Single photon emission computed tomography (SPECT) is being investigated for imaging inside radiation therapy treatment rooms to localize biological targets. Here, computer simulations were used to analyze locational and directional dependencies in localization errors and to assess the effects of spatial resolution modeling and observer normalization on localization performance.

METHODS

SPECT images of the XCAT phantom, containing 12 hot tumors, were reconstructed with detector response function compensation (DRC) and without DRC (nDRC). Numerical observers were forced to select the most suspicious tumor location, using normalized cross correlation (NXC) or un-normalized cross correlation (XC), from 3 cm diameter search volumes that each contained only one tumor. For each tumor site, localization was optimized as a function of the iteration number and postreconstruction smoothing. Localization error, the distance between true and estimated tumor positions, was calculated across the ensembles of 80 images. Direction-dependent localization bias and precision were estimated from the image ensemble.

RESULTS

For the six superficial tumors in close proximity to the detector trajectory, mean localization errors were < 2 mm and were lowest or comparable using DRC-NXC, though differences from DRC-XC and nDRC-NXC were not statistically significant. DRC-NXC did provide statistically significantly better localization than nDRC-XC for five of these six tumors. At the other six sites where attenuation was more severe and the distance was generally greater between the tumor and detector, DRC typically did not show better localization than nDRC. Observer normalization improved the localization substantially for a tumor near the hotter heart. Localization errors were anisotropic and dependent on tumor location relative to the detector trajectory.

CONCLUSIONS

This computer-simulation study compared localization performance for normalized and un-normalized numerical observers, which were used to estimate tumor positions in SPECT images, reconstructed with and without DRC. For tumors localized to < 2 mm on average, which are good candidates for SPECT-guided radiation therapy, localization performance typically improved by compensating for the detector response function and by using a normalized observer. The observed direction-dependent localization errors have important implications for radiation therapy and are relevant to SPECT imaging in general.

On-board SPECT for localizing functional targets: a simulation study

Single photon emission computed tomography (SPECT) was investigated for imaging on-board radiation therapy machines in order to localize functional and molecular targets. A computer-simulated female NCAT phantom was positioned supine on a flat-top treatment couch. Twenty tumor locations were defined in the upper torso. The eight lung tumors were subject to the effects of respiratory motion. Tumor diameters of 10.8, 14.4, and 21.6 mm were simulated for tumor-to-background ratios of 3:1 and 6:1 that are characteristic of the radiotracer 99mTc-sestamibi. Projection images representing scan times of 4, 8, and 20 min were simulated for an anterior, half-circular trajectory. Images were reconstructed with attenuation correction by ordered-subsets expectation maximization (OSEM) using six subsets and five iterations. Contrast-to-noise ratios (CNRs) were calculated from ensembles of 25 images. Cross correlation with a noise-free tumor template was used to select the most suspicious tumor location within a 14.4-mm-radius search volume surrounding each tumor, with only that one tumor in each search volume. Localization accuracy was assessed by calculating average distances between measured and true tumor locations. Localization accuracy and CNRs were strongly affected by tumor location relative to the detector trajectory. For example, CNR values near the chest wall were greater by a factor of 3.5 than for tumors near the spine and posterior ribs, a much greater effect than the factor of 1.6 difference in CNR between 6:1 and 3:1 tumor uptakes. Typically, tumors of 6:1 uptake were localized as accurately with 4 min of scan time as tumors of 3:1 uptake that had been imaged for 20 min. Using 4 min scans, 14.4 and 21.6 mm anterior tumors of 6:1 uptake were localized within 2 mm. These results suggest that SPECT, on-board radiation therapy machines, may be a viable modality for localizing certain functional and molecular targets using relatively short scan times.

Evaluation of tilted cone-beam CT orbits in the development of a dedicated hybrid mammotomograph

A compact dedicated 3D breast SPECT-CT (mammotomography) system is currently under development. In its initial prototype, the cone-beam CT sub-system is restricted to a fixed-tilt circular rotation around the patient's pendant breast. This study evaluated stationary-tilt angles for the CT sub-system that will enable maximal volumetric sampling and viewing of the breast and chest wall. Images of geometric/anthropomorphic phantoms were acquired using various fixed-tilt circular and 3D sinusoidal trajectories. The iteratively reconstructed images showed more distortion and attenuation coefficient inaccuracy from tilted cone-beam orbits than from the complex trajectory. Additionally, line profiles illustrated cupping artifacts in planes distal to the central plane of the tilted cone-beam, otherwise not apparent for images acquired with complex trajectories. This indicates that undersampled cone-beam data may be an additional cause of cupping artifacts. High-frequency objects could be distinguished for all trajectories, but their shapes and locations were corrupted by out-of-plane frequency information. Although more acrylic balls were visualized with a fixed-tilt and nearly flat cone-beam at the posterior of the breast, 3D complex trajectories have less distortion and more complete sampling throughout the reconstruction volume. While complex trajectories would ideally be preferred, negatively fixed-tilt source-detector configuration demonstrates minimally distorted patient images.

Incorporation of system resolution compensation (RC) in the ordered-subset transmission (OSTR) algorithm for transmission imaging in SPECT

In order to reconstruct attenuation maps with improved spatial resolution and quantitative accuracy, we developed an approximate method of incorporating system resolution compensation (RC) in the ordered-subset transmission (OSTR) algorithm for transmission reconstruction. Our method approximately models the blur caused by the finite intrinsic detector resolution, the nonideal source collimation and detector collimation. We derived the formulation using the optimization transfer principle as in the derivation of the OSTR algorithm. The formulation includes one forward-blur step and one back-blur step, which do not severely slow down reconstruction. The formulation could be applicable to various transmission geometries, such as point-source, line-source, and sheet-source systems. Through computer simulations of the MCAT phantom and transmission measurements of the air-filled Data Spectrum Deluxe single photo emission computed tomography (SPECT) Phantom on a system which employed a cone-beam geometry and a system which employed a scanning-line-source geometry, we showed that incorporation of RC increased spatial resolution and improved the quantitative accuracy of reconstruction. In simulation studies, attenuation maps reconstructed with RC correction improved the quantitative accuracy of emission reconstruction.

Characterization and suppression of edge and aliasing artefacts in iterative x-ray CT reconstruction

For the purpose of obtaining x-ray tomographic images, statistical reconstruction (SR) provides a general framework with possible advantages over analytical algorithms such as filtered backprojection (FBP) in terms of flexibility, resolution, contrast and image noise. However, SR images may be seriously affected by some artefacts that are not present in FBP images. These artefacts appear as aliasing patterns and as severe overshoots in the areas of sharp intensity transitions ('edge artefacts'). We characterize this inherent property of iterative reconstructions and hypothesize how discretization errors during reconstruction contribute to the formation of the artefacts. An adequate solution to the problem is to perform the reconstructions on an image grid that is finer than that typically employed for FBP reconstruction, followed by a downsampling of the resulting image to a granularity normally used for display. Furthermore, it is shown that such a procedure is much more effective than post-filtering of the reconstructions. Resulting SR images have superior noise-resolution trade-off compared to FBP, which may facilitate dose reduction during CT examinations.

Suppression of intensity transition artifacts in statistical x-ray computer tomography reconstruction through Radon inversion initialization

Statistical reconstruction (SR) methods provide a general and flexible framework for obtaining tomographic images from projections. For several applications SR has been shown to outperform analytical algorithms in terms of resolution-noise trade-off achieved in the reconstructions. A disadvantage of SR is the long computational time required to obtain the reconstructions, in particular when large data sets characteristic for x-ray computer tomography (CT) are involved. As was shown recently, by combining statistical methods with block iterative acceleration schemes [e.g., like in the ordered subsets convex (OSC) algorithm], the reconstruction time for x-ray CT applications can be reduced by about two orders of magnitude. There are, however, some factors lengthening the reconstruction process that hamper both accelerated and standard statistical algorithms to similar degree. In this simulation study based on monoenergetic and scatter-free projection data, we demonstrate that one of these factors is the extremely high number of iterations needed to remove artifacts that can appear around high-contrast structures. We also show (using the OSC method) that these artifacts can be adequately suppressed if statistical reconstruction is initialized with images generated by means of Radon inversion algorithms like filtered back projection (FBP). This allows the reconstruction time to be shortened by even as much as one order of magnitude. Although the initialization of the statistical algorithm with FBP image introduces some additional noise into the first iteration of OSC reconstruction, the resolution-noise trade-off and the contrast-to-noise ratio of final images are not markedly compromised.

An EM algorithm for estimating SPECT emission and transmission parameters from emissions data only

A maximum-likelihood (ML) expectation-maximization (EM) algorithm (called EM-IntraSPECT) is presented for simultaneously estimating single photon emission computed tomography (SPECT) emission and attenuation parameters from emission data alone. The algorithm uses the activity within the patient as transmission tomography sources, with which attenuation coefficients can be estimated. For this initial study, EM-IntraSPECT was tested on computer-simulated attenuation and emission maps representing a simplified human thorax as well as on SPECT data obtained from a physical phantom. Two evaluations were performed. First, to corroborate the idea of reconstructing attenuation parameters from emission data, attenuation parameters (mu) were estimated with the emission intensities (lambda) fixed at their true values. Accurate reconstructions of attenuation parameters were obtained. Second, emission parameters lambda and attenuation parameters mu were simultaneously estimated from the emission data alone. In this case there was crosstalk between estimates of lambda and mu and final estimates of lambda and mu depended on initial values. Estimates degraded significantly as the support extended out farther from the body, and an explanation for this is proposed. In the EM-IntraSPECT reconstructed attenuation images, the lungs, spine, and soft tissue were readily distinguished and had approximately correct shapes and sizes. As compared with standard EM reconstruction assuming a fix uniform attenuation map, EM-IntraSPECT provided more uniform estimates of cardiac activity in the physical phantom study and in the simulation study with tight support, but less uniform estimates with a broad support. The new EM algorithm derived here has additional applications, including reconstructing emission and transmission projection data under a unified statistical model.