Carey E. Floyd

Inverse Monte Carlo: A Unified Reconstruction Algorithm for SPECT

Inverse Monte Carlo (IMOC) is presented as a unified reconstruction algorithm for Emission Computed Tomography (ECT) providing simultaneous compensation for scatter, attenuation, and the variation of collimator resolution with depth. The technique of inverse Monte Carlo is used to find an inverse solution to the photon transport equation (an integral equation for photon flux from a specified source) for a parameterized source and specific boundary conditions. The system of linear equations so formed is solved to yield the source activity distribution for a set of acquired projections. For the studies presented here, the equations are solved using the EM (Maximum Likelihood) algorithm although other solution algorithms, such as Least Squares, could be employed. While the present results specifically consider the reconstruction of camera-based Single Photon Emission Computed Tomographic (SPECT) images, the technique is equally valid for Positron Emission Tomography (PET) if a Monte Carlo model of such a system is used. As a preliminary evaluation, experimentally acquired SPECT phantom studies for imaging Tc-99m (140 keV) are presented which demonstrate the quantitative compensation for scatter and attenuation for a two dimensional (single slice) reconstruction. The algorithm may be expanded in a straight forward manner to full three dimensional reconstruction including compensation for out of plane scatter.

Bayesian reconstruction and use of anatomical a priori information for emission tomography

A Bayesian method is presented for simultaneously segmenting and reconstructing emission computed tomography (ECT) images and for incorporating high-resolution, anatomical information into those reconstructions. The anatomical information is often available from other imaging modalities such as computed tomography (CT) or magnetic resonance imaging (MRI). The Bayesian procedure models the ECT radiopharmaceutical distribution as consisting of regions, such that radiopharmaceutical activity is similar throughout each region. It estimates the number of regions, the mean activity of each region, and the region classification and mean activity of each voxel. Anatomical information is incorporated by assigning higher prior probabilities to ECT segmentations in which each ECT region stays within a single anatomical region. This approach is effective because anatomical tissue type often strongly influences radiopharmaceutical uptake. The Bayesian procedure is evaluated using physically acquired single-photon emission computed tomography (SPECT) projection data and MRI for the three-dimensional (3-D) Hoffman brain phantom. A clinically realistic count level is used. A cold lesion within the brain phantom is created during the SPECT scan but not during the MRI to demonstrate that the estimation procedure can detect ECT structure that is not present anatomically.

Application of the mutual information criterion for feature selection in computer-aided diagnosis.

The purpose of this study was to investigate an information theoretic approach to feature selection for computer-aided diagnosis (CAD). The approach is based on the mutual information (MI) concept. MI measures the general dependence of random variables without making any assumptions about the nature of their underlying relationships. Consequently, MI can potentially offer some advantages over feature selection techniques that focus only on the linear relationships of variables. This study was based on a database of statistical texture features extracted from perfusion lung scans. The ultimate goal was to select the optimal subset of features for the computer-aided diagnosis of acute pulmonary embolism (PE). Initially, the study addressed issues regarding the approximation of MI in a limited dataset as it is often the case in CAD applications. The MI selected features were compared to those features selected using stepwise linear discriminant analysis and genetic algorithms for the same PE database. Linear and nonlinear decision models were implemented to merge the selected features into a final diagnosis. Results showed that the MI is an effective feature selection criterion for nonlinear CAD models overcoming some of the well-known limitations and computational complexities of other popular feature selection techniques in the field.

Computer‐assisted detection of mammographic masses: A template matching scheme based on mutual information

The purpose of this study was to develop a knowledge-based scheme for the detection of masses on digitized screening mammograms. The computer-assisted detection (CAD) scheme utilizes a knowledge databank of mammographic regions of interest (ROIs) with known ground truth. Each ROI in the databank serves as a template. The CAD system follows a template matching approach with mutual information as the similarity metric to determine if a query mammographic ROI depicts a true mass. Based on their information content, all similar ROIs in the databank are retrieved and rank-ordered. Then, a decision index is calculated based on the querys best matches. The decision index effectively combines the similarity indices and ground truth of the best-matched templates into a prediction regarding the presence of a mass in the query mammographic ROI. The system was developed and evaluated using a database of 1465 ROIs extracted from the Digital Database for Screening Mammography. There were 809 ROIs with confirmed masses (455 malignant and 354 benign) and 656 normal ROIs. CAD performance was assessed using a leave-one-out sampling scheme and Receiver Operating Characteristics analysis. Depending on the formulation of the decision index, CAD performance as high as A(zeta) = 0.87 +/- 0.01 was achieved. The CAD detection rate was consistent for both malignant and benign masses. In addition, the impact of certain implementation parameters on the detection accuracy and speed of the proposed CAD scheme was studied in more detail.

Energy and spatial distribution of multiple order Compton scatter in SPECT: a Monte Carlo investigation

Energy and spatial projection distributions were simulated for gamma camera imaging of multiple order Compton scattered photons. SPECT imaging of a line source of radioactivity located in a water filled cylindrical phantom was modelled using Monte Carlo techniques. Photon trajectories were followed from emission to detection including the effects of all physical interactions and the resulting energy spectra and spatial projections were sorted as a function of the number of times the photon underwent Compton scattering before detection. Analysis of energy spectra demonstrates that Compton events up to second order overlap with the non-scattered events and distributions are peaked at lower energies as the scattering order increases. Analysis of spatial projections shows that, with increasing order, Compton events produce tails on the line spread function which progress from roughly exponential to nearly flat distributions. The use of Monte Carlo modelling thus allows a detailed investigation of the spatial and energy distribution of Compton scatter which could not be performed using present experimental techniques.

Evaluation of information-theoretic similarity measures for content-based retrieval and detection of masses in mammograms

The purpose of this study was to evaluate image similarity measures employed in an information-theoretic computer-assisted detection (IT-CAD) scheme. The scheme was developed for content-based retrieval and detection of masses in screening mammograms. The study is aimed toward an interactive clinical paradigm where physicians query the proposed IT-CAD scheme on mammographic locations that are either visually suspicious or indicated as suspicious by other cuing CAD systems. The IT-CAD scheme provides an evidence-based, second opinion for query mammographic locations using a knowledge database of mass and normal cases. In this study, eight entropy-based similarity measures were compared with respect to retrieval precision and detection accuracy using a database of 1820 mammographic regions of interest. The IT-CAD scheme was then validated on a separate database for false positive reduction of progressively more challenging visual cues generated by an existing, in-house mass detection system. The study showed that the image similarity measures fall into one of two categories; one category is better suited to the retrieval of semantically similar cases while the second is more effective with knowledge-based decisions regarding the presence of a true mass in the query location. In addition, the IT-CAD scheme yielded a substantial reduction in false-positive detections while maintaining high detection rate for malignant masses.

Scatter Compensation Techniques for SPECT

Compton scattered photons included within the photopeak pulse-height window decrease the image contrasts of lesions. Furthermore, in the absence of an effective compensation procedure, the accuracy of the SPECT measurement is reduced. In the following sections the effect of scatter on SPECT is reviewed, and the influence of scattered photons on the effective linear attenuation coefficient used with multiplicative attenuation compensation methods is described. Criteria for evaluating scatter compensation procedures are proposed, and approaches to reducing the effect of scatter on SPECT imaging are described.

Cone beam collimation for single photon emission computed tomography: analysis, simulation, and image reconstruction using filtered backprojection

This paper presents an analysis of two cone beam configurations (having focal lengths of 40 and 60 cm) for the acquisition of single photon emission computed tomography (SPECT) projection data. A three-dimensional filtered backprojection algorithm is used to reconstruct SPECT images of cone beam projection data obtained using Monte Carlo simulations. The mathematical analysis resulted in on-axis point source sensitivities (calculated for a distance of 15 cm from the collimator surface) for cone beam configurations that were 1.4-3 times the sensitivities of parallel-hole and fan beam geometries having similar geometric resolutions. Cone beam collimation offers the potential for improved sensitivity for SPECT devices using large-field-of-view scintillation cameras.

Self-organizing map for cluster analysis of a breast cancer database

The purpose of this study was to identify and characterize clusters in a heterogeneous breast cancer computer-aided diagnosis database. Identification of subgroups within the database could help elucidate clinical trends and facilitate future model building. A self-organizing map (SOM) was used to identify clusters in a large (2258 cases), heterogeneous computer-aided diagnosis database based on mammographic findings (BI-RADS) and patient age. The resulting clusters were then characterized by their prototypes determined using a constraint satisfaction neural network (CSNN). The clusters showed logical separation of clinical subtypes such as architectural distortions, masses, and calcifications. Moreover, the broad categories of masses and calcifications were stratified into several clusters (seven for masses and three for calcifications). The percent of the cases that were malignant was notably different among the clusters (ranging from 6 to 83%). A feed-forward back-propagation artificial neural network (BP-ANN) was used to identify likely benign lesions that may be candidates for follow up rather than biopsy. The performance of the BP-ANN varied considerably across the clusters identified by the SOM. In particular, a cluster (#6) of mass cases (6% malignant) was identified that accounted for 79% of the recommendations for follow up that would have been made by the BP-ANN. A classification rule based on the profile of cluster #6 performed comparably to the BP-ANN, providing approximately 25% specificity at 98% sensitivity. This performance was demonstrated to generalize to a large (2177) set of cases held-out for model validation.

Reconstruction of SPECT images using generalized matrix inverses

Generalized matrix inverses are used to estimate source activity distributions from single photon emission computed tomography (SPECT) projection measurements. Image reconstructions for a numerical simulation and a clinical brain study are examined. The photon flux from the source region and photon detection by the gamma camera are modeled by matrices which are computed by Monte Carlo methods. The singular value decompositions (SVDs) of these matrices give considerable insight into the SPECT image reconstruction problem and the SVDs are used to form approximate generalized matrix inverses. Tradeoffs between resolution and error in estimating source voxel intensities are discussed, and estimates of these errors provide a robust means of stabilizing the solution to the ill-posed inverse problem. In addition to its quantitative clinical applications, the generalized matrix inverse method may be a useful research tool for tasks such as evaluating collimator design and optimizing gamma camera motion.