Soo Mee Kim

Fully three-dimensional OSEM-based image reconstruction for Compton imaging using optimized ordering schemes.

Although the ordered subset expectation maximization (OSEM) algorithm does not converge to a true maximum likelihood solution, it is known to provide a good solution if the projections that constitute each subset are reasonably balanced. The Compton scattered data can be allocated to subsets using scattering angles (SA) or detected positions (DP) or a combination of the two (AP (angles and positions)). To construct balanced subsets, the data were first arranged using three ordering schemes: the random ordering scheme (ROS), the multilevel ordering scheme (MLS) and the weighted-distance ordering scheme (WDS). The arranged data were then split into J subsets. To compare the three ordering schemes, we calculated the coefficients of variation (CVs) of angular and positional differences between the arranged data and the percentage errors between mathematical phantoms and reconstructed images. All ordering schemes showed an order-of-magnitude acceleration over the standard EM, and their computation times were similar. The SA-based MLS and the DP-based WDS led to the best-balanced subsets (they provided the largest angular and positional differences for SA- and DP-based arrangements, respectively). The WDS exhibited minimum CVs for both the SA- and DP-based arrangements (the deviation in mean angular and positional differences between the ordered subsets was smallest). The combination of AP and WDS yielded the best results with the lowest percentage errors by providing larger and more uniform angular and positional differences for the SA and DP arrangements, and thus, is probably optimal Compton camera reconstruction using OSEM.

Gap compensation during PET image reconstruction by constrained, total variation minimization

PURPOSE Positron emission tomography (PET) is a noninvasive molecular imaging tool with various clinical and preclinical applications. The polygonal structure of small-diameter PET scanners that are designed for specific purposes can lead to gaps between the detector modules and result in loss of PET data during measurement. In the current study, the authors applied the compressed sensing (CS)-based total variation (TV) minimization method to PET image reconstructions to reduce the artifacts caused by gaps in small-diameter PET systems. METHODS The first step in each iteration estimates whether an image is consistent with the measured PET data using the existing common reconstruction algorithms (ART, OSEM, and RAMLA). The second step recovers sparsity in the gradient domain of the image by minimizing the TV of an estimated image. The authors evaluated the gap-compensable reconstruction algorithms with uniform disk and Shepp-Logan phantoms by simulating sinograms which contained Poisson random noise and a data loss due to detector gaps. In addition, these methods were applied to real high resolution research tomography (HRRT)-like sinograms of human brain and uniform phantom. A comparison with other methods for gap compensation prior to or during image reconstruction was also made. Quantitative evaluations were performed by computing the uniformity, root mean squared error, and difference between the reconstructed images of nongapped and gapped sinograms. RESULTS The simulation results showed that the gap-compensable methods incorporating TV minimization could control gap artifacts, as well as Poisson random noise. In particular, OSEM-TV and RAMLA-TV showed distinct potential via the properties of convergence and robustness to different noise levels and gap angle. CONCLUSIONS A TV minimization strategy incorporated into commonly used PET reconstruction algorithms was useful for reducing the occurrence of artifacts due to gaps between detector modules in small-diameter PET scanners.

Multitracing Capability of Double-Scattering Compton Imager With NaI(Tl) Scintillator Absorber

The Compton camera can provide 3-D images of radioactive material distribution based on a single measurement at a fixed position. The Compton camera also can image several different kinds of radioactive materials simultaneously, by means of the “multitracing” capability. In the present study, this multitracing capability was tested for a double-scattering-type Compton camera, or Double-Scattering Compton Imager (DOCI), which utilizes two double-sided silicon strip detectors (DSSDs) and one NaI(Tl) scintillation detector. Our experimental result shows that the 137Cs and 60Co gamma sources can be clearly distinguished in 2-D and 3-D Compton images, and that there is no significant interference between the two gamma sources. The imaging resolutions were determined to be 6.2 and 4.7 mm FWHM for the 137Cs (662 keV) and 60Co (1332 keV) point sources at 4 cm, respectively. The angular resolutions, determined from the angular resolution measure (ARM) distributions, were 7.3° and 6.5° for the source energies of 662 and 1332 keV, respectively. The DOCI remains under development; its imaging resolution will be further improved with the incorporation of more sophisticated detectors and the related electronics, including a faster scintillation detector (LYSO) and higher-spatial-resolution position-sensitive detectors.

Three-dimensional edge-preserving regularization for Compton camera reconstruction

Compton imaging is often recognized as a potentially more valuable 3-D technique than conventional emission tomography. However, due to the inherent complexity of massive data set computations for the conical projection-backprojection operation, most reconstruction algorithms have been based on analytical methods rather than statistical methods. In this paper, we investigate a maximum a posteriori (MAP) approach to Compton camera reconstruction, which provides reconstructions with superior noise characteristics compared to analytical methods. In order to preserve edges that can occur occasionally in the underlying object, we use a convex-nonquadratic smoothing prior and apply to a row-action based regularized maximum likelihood method, which is provably convergent to a true MAP solution. Our preliminary results indicate that, although the statistical methods considered in this paper are not as fast as analytical methods, they have a great potential to improve quantitative accuracy in Compton imaging.

Comparison Between Pre-Log and Post-Log Statistical Models in Ultra-Low-Dose CT Reconstruction

X-ray detectors in clinical computed tomography (CT) usually operate in current-integrating mode. Their complicated signal statistics often lead to intractable likelihood functions for practical use in model-based image reconstruction (MBIR). It is therefore desirable to design simplified statistical models without losing the essential factors. Depending on whether the CT transmission data are logarithmically transformed, pre-log and post-log models are two major categories of choices in CT MBIR. Both being approximations, it remains an open question whether one model can notably improve image quality over the other on real scanners. In this study, we develop and compare several pre-log and post-log MBIR algorithms under a unified framework. Their reconstruction accuracy based on simulation and clinical datasets are evaluated. The results show that pre-log MBIR can achieve notably better quantitative accuracy than post-log MBIR in ultra-low-dose CT, although in less extreme cases, post-log MBIR with handcrafted pre-processing remains a competitive alternative. Pre-log MBIR could play a growing role in emerging ultra-low-dose CT applications.X-ray detectors in clinical computed tomography (CT) usually operate in current-integrating mode. Their complicated signal statistics often lead to intractable likelihood functions for practical use in model-based image reconstruction (MBIR). It is therefore desirable to design simplified statistical models without losing the essential factors. Depending on whether the CT transmission data are logarithmically transformed, pre-log and post-log models are two major categories of choices in CT MBIR. Both being approximations, it remains an open question whether one model can notably improve image quality over the other on real scanners. In this study, we develop and compare several pre-log and post-log MBIR algorithms under a unified framework. Their reconstruction accuracy based on simulation and clinical datasets are evaluated. The results show that pre-log MBIR can achieve notably better quantitative accuracy than post-log MBIR in ultra-low-dose CT, although in less extreme cases, post-log MBIR with handcrafted pre-processing remains a competitive alternative. Pre-log MBIR could play a growing role in emerging ultra-low-dose CT applications.

Analysis of statistical models for iterative reconstruction of extremely low-dose CT data

In order to reduce CT radiation dose, there have been numerous efforts to develop low-dose acquisition protocols as well as noise reduction methods such as data denoising and iterative reconstruction. In this study, we analyze the first and second order statistics of post-log CT data and the resulting impact on iterative image reconstruction for extremely low-dose CT acquisitions. We performed a CT simulation incorporating polychromatic forward projection and realistic levels of quantum and electronic noise. We performed N=1000 simulations of a chest phantom to analyze the impact of processing steps on the statistics of post-log data. We investigated the impact of two non-positivity correction methods, threshold and mean-preserving filter. And, we analyzed the bias and variance of different weighting terms and performed weighted least squares reconstruction with these different weights. For the simulation of an extremely low dose chest acquisition with 80 kVp and 0.5 mAs, the mean-preserving filter reduced the mean bias of post-log sinogram by roughly seven times compared to the threshold method. The WLS reconstructed images using simple weighting terms that ignored the effect of non-positive correction lead to limited improvements in image quality. Accurate weighting terms including electronic noise and the variance change from MPF provided superior images, especially in highly attenuating regions where bias reductions of ~17% were achieved compared to simple weighting matrices. Appropriate selection of the non-positivity correction method is essential for low flux CT data processing. The proposed method for estimating the weighting matrix with electronic noise and the effect of pre-corrections leads to some improvements in variance estimation for post-log CT data, although it has potential for further improvement.

Fully three-dimensional image reconstruction for compton imaging using ordered subsets of conical projection data

The Compton camera has recently been recognized as a promising three-dimensional imaging modality with higher sensitivity and unlimited field-of-view. Due to computational limitations, however, it has been of a difficult problem to develop reconstruction algorithms with good. In this study, we propose efficient methods for implementing the OSEM (ordered-subsets expectation-maximization) algorithm for Compton camera reconstruction, and investigate three different schemes for grouping Compton scattered data into ordered subsets. The first is to group the data according to a pre-set order of scattering angles, the second is to group the possible combinations of detected position pairs in the scatterer and the absorber, and the third is to combine the first and second methods. According to our experimental results, all of the three grouping schemes exhibit similar performance in terms of the quantitative accuracy and computational efficiency. Our results show that the OSEM algorithm applied to the Compton camera provides an order improvement in speed of execution while retaining overall quality of the image reconstructed by the standard EM algorithm.

Resolution recoverable statistical listmode reconstruction using depth dependent point spread function for Compton camera

A Compton camera is an imaging system for three-dimensional (3D) distribution of gamma emitting sources based on Compton scattering interaction. The measurement error on energies and positions directly leads to uncertainties on the formation of cones and degrades the spatial resolution of the reconstructed images. Mostly the limited energy resolution, Doppler broadening and position segmentation of detectors cause angular and positional uncertainties on measurements. Since the conical surfaces are delocalized by angular and positional uncertainties into image space, degradation of spatial resolution may be severe depending on the distance (or depth) from the Compton camera. In order to enhance the deteriorated spatial resolution due to angular and positional uncertainties, this study investigates 3D Gaussian point spread function (PSF) incorporable into listmode ordered subset expectation maximization (LMOSEM) as a part of system matrix. Especially the depth-dependent PSF is applied as resolution recovery (RR) technique by image-space convolution operation. We investigated two different RR approaches: one (denoted by LMOSEM-RR-F) is when the convolution is performed in forward projection step only, and the other (denoted by LMOSEM-RR-FB) is when it is performed in both forward and backward projection steps. Using Monte Carlo data for 7 point sources at different depth from the Compton camera, the fitted axial and radial FWHM functions were obtained as FWHMaxial (i)=0.2442i+1.054 and FWHMradial (i)=0.2369i–1.005, respectively. The simulation results showed that both RR approaches with depth dependent PSF gave an improvement on spatial resolution comparing to LMOSEM without RR techniques. Although LMOSEM-RR-F provided better resolution than LMOSEM-RR-FB, LMOSEM-RR-FB could still be useful for low counting statistics in measurement.

Analytic simulator and image generator of multiple-scattering Compton camera for prompt gamma ray imaging

For prompt gamma ray imaging for biomedical applications and environmental radiation monitoring, we propose herein a multiple-scattering Compton camera (MSCC). MSCC consists of three or more semiconductor layers with good energy resolution, and has potential for simultaneous detection and differentiation of multiple radio-isotopes based on the measured energies, as well as three-dimensional (3D) imaging of the radio-isotope distribution. In this study, we developed an analytic simulator and a 3D image generator for a MSCC, including the physical models of the radiation source emission and detection processes that can be utilized for geometry and performance prediction prior to the construction of a real system. The analytic simulator for a MSCC records coincidence detections of successive interactions in multiple detector layers. In the successive interaction processes, the emission direction of the incident gamma ray, the scattering angle, and the changed traveling path after the Compton scattering interaction in each detector, were determined by a conical surface uniform random number generator (RNG), and by a Klein–Nishina RNG. The 3D image generator has two functions: the recovery of the initial source energy spectrum and the 3D spatial distribution of the source. We evaluated the analytic simulator and image generator with two different energetic point radiation sources (Cs-137 and Co-60) and with an MSCC comprising three detector layers. The recovered initial energies of the incident radiations were well differentiated from the generated MSCC events. Correspondingly, we could obtain a multi-tracer image that combined the two differentiated images. The developed analytic simulator in this study emulated the randomness of the detection process of a multiple-scattering Compton camera, including the inherent degradation factors of the detectors, such as the limited spatial and energy resolutions. The Doppler-broadening effect owing to the momentum distribution of electrons in Compton scattering was not considered in the detection process because most interested isotopes for biomedical and environmental applications have high energies that are less sensitive to Doppler broadening. The analytic simulator and image generator for MSCC can be utilized to determine the optimal geometrical parameters, such as the distances between detectors and detector size, thus affecting the imaging performance of the Compton camera prior to the development of a real system.

Mixed Confidence Estimation for Iterative CT Reconstruction

Dynamic (4D) CT imaging is used in a variety of applications, but the two major drawbacks of the technique are its increased radiation dose and longer reconstruction time. Here we present a statistical analysis of our previously proposed Mixed Confidence Estimation (MCE) method that addresses both these issues. This method, where framed iterative reconstruction is only performed on the dynamic regions of each frame while static regions are fixed across frames to a composite image, was proposed to reduce computation time. In this work, we generalize the previous method to describe any application where a portion of the image is known with higher confidence (static, composite, lower-frequency content, etc.) and a portion of the image is known with lower confidence (dynamic, targeted, etc). We show that by splitting the image space into higher and lower confidence components, MCE can lower the estimator variance in both regions compared to conventional reconstruction. We present a theoretical argument for this reduction in estimator variance and verify this argument with proof-of-principle simulations. We also propose a fast approximation of the variance of images reconstructed with MCE and confirm that this approximation is accurate compared to analytic calculations of and multi-realization image variance. This MCE method requires less computation time and provides reduced image variance for imaging scenarios where portions of the image are known with more certainty than others allowing for potentially reduced radiation dose and/or improved dynamic imaging.