R.E. Coleman

Parameter estimation of finite mixtures using the EM algorithm and information criteria with application to medical image processing

A method for parameter estimation in image classification or segmentation is studied within the statistical frame of finite mixture distributions. The method models an image as a finite mixture. Each mixture component corresponds to an image class. Each image class is characterized by parameters, such as the intensity mean, the standard deviation, and the number of image pixels in that class. The method uses a maximum likelihood (ML) approach to estimate the parameters of each class and employs information criteria of Akaike (AIC) and/or Schwarz and Rissanen (MDL) to determine the number of classes in the image. In computing the ML solution of the mixture, the method adopts the expectation maximization (EM) algorithm. The initial estimation and convergence of the ML-EM algorithm were studied. The accuracy in determining the number of image classes using AIC and MDL is compared. The MDL criterion performed better than the AIC criterion. A modified MDL showed further improvement. >

Simultaneous compensation for attenuation, scatter and detector response for SPECT reconstruction in three dimensions

A three-dimensional reconstruction method for simultaneous compensation of attenuation, scatter and distance-dependent detector response for single photon emission computed tomography is described and tested by experimental studies. The method determines the attenuation factors recursively along each projection ray starting at the intersected source voxel closest to the detector. The method substracts the scatter energy window data from the primary energy window data for scatter compensation. The detector response is modelled to be spatially invariant at a constant distance from the detector. The method convolves source distribution with the modelled response function to compensate for the smoothed by use of a non-uniform entropy prior to searching for the maximum a posteriori probability solution. The method was tested using projections acquired from a chest phantom by a three-headed detector system with parallel hole collimators. An improvement was shown in image noise, recognition of object sizes and shapes, and quantification of concentration ratios.

FDG-PET in the selection of brain lesions for biopsy.

The CT-guided stereotaxic needle biopsy has become a widely used procedure in the diagnostic evaluation of intracranial lesions including tumors. Conventional CT or MR frequently defines the anatomic regions of abnormality, which may be multiple lesions or a single lesion that is heterogeneous in cellular composition owing to the topographic variation of cellular constituency or the combination of active disease, nonspecific inflammation, necrosis, and/or edema. In these cases, selection of the most appropriate site for a successful diagnostic needle biopsy can be difficult. In three patients, we have used [18F]fluorodeoxyglucose (FDG) positron emission tomography (PET) to determine the site most likely to provide a diagnostic biopsy result. In the first patient, who presented with confusion, multiple biopsies from the temporal lobe, based on MR abnormalities, revealed only reactive gliosis and edema. Repeat biopsy directed by PET revealed an anaplastic astrocytoma. In a second patient, PET allowed us to differentiate radiation effect from active metastatic breast cancer. In the third patient, who presented with a grand mal seizure, biopsy of a CT-defined hypodense region demonstrated lymphocytosis. Metabolism of FDG was normal or increased in areas of Aspergillus encephalitis at autopsy. These preliminary studies suggest a complementary role for FDG-PET and CT or MR in selected patients for defining the intracranial site most likely to yield a positive biopsy result.

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.

FDG-PET in pediatric posterior fossa brain tumors

Seventeen pediatric patients with posterior fossa brain tumors were studied with 2-[18F]fluoro-2-deoxy-D-glucose (FDG) and positron emission tomography (PET). The FDG uptake was ranked by two observers, and the results were correlated with tumor histology. Increased FDG uptake was associated with more malignant and aggressive tumor types. Heterogeneity of FDG uptake was associated with previous therapy, including radiation therapy and chemotherapy. 2-[18F]Fluoro-2-deoxy-D-glucose PET will likely be an important adjunct in the management of pediatric posterior fossa tumors, much as in adult patients with brain tumors.

Solid geometry-based object model for Monte Carlo simulated emission and transmission tomographic imaging systems

An object model based on combinations of object primitives is proposed for Monte Carlo simulated emission and transmission tomographic imaging systems. The primitives include ellipsoids, elliptic cylinders, tapered elliptic cylinders, rectangular solids, and their subsets: half, quarter, and eighth. The probability of a photon surviving interactions with the phantom medium is used as a weight for variance reduction. Calculation of the probability can be computationally intensive without properly organizing the inclusion of subregions within larger regions. A tree data structure is introduced to organize this inclusion relationship and used as the basis for two computationally efficient schemes for determining the intersection locations of a photon path with primitives and for identifying the attenuation coefficients for adjacent intersections for the survival probability computation. The approach has been validated by emission as well as transmission simulations. A thorax phantom containing overlapped ellipsoids and a heart composed of twelve overlapped quarter ellipsoids are employed to demonstrate the capability of the model.

Simultaneous reconstruction, segmentation, and edge enhancement of relatively piecewise continuous images with intensity-level information

A multinomial image model is proposed which uses intensity-level information for reconstruction of contiguous image regions. The intensity-level information assumes that image intensities are relatively constant within contiguous regions over the image-pixel array and that intensity levels of these regions are determined either empirically or theoretically by information criteria. These conditions may be valid, for example, for cardiac blood-pool imaging, where the intensity levels (or radionuclide activities) of myocardium, blood-pool, and background regions are distinct and the activities within each region of muscle, blood, or background are relatively uniform. To test the model, a mathematical phantom over a 64 x 64 array was constructed. The phantom had three contiguous regions. Each region had a different intensity level. Measurements from the phantom were simulated using an emission-tomography geometry. Fifty projections were generated over 180 degrees, with 64 equally spaced parallel rays per projection. Projection data were randomized to contain Poisson noise. Image reconstructions were performed using an iterative maximum a posteriori probability procedure. The contiguous regions corresponding to the three intensity levels were automatically segmented. Simultaneously, the edges of the regions were sharpened. Noise in the reconstructed images was significantly suppressed. Convergence of the iterative procedure to the phantom was observed. Compared with maximum likelihood and filtered-backprojection approaches, the results obtained using the maximum a posteriori probability with the intensity-level information demonstrated qualitative and quantitative improvement in localizing the regions of varying intensities.

On Reconstruction and Segmentation of Piecewise Continous Images

We evaluate an image model for simultaneous reconstruction and segmentation of piecewise continuous images. The model assumes that the intensities of the piecewise continuous image are relatively constant within contiguous regions and that the intensity levels of these regions can be determined either empirically or theoretically before reconstruction. The assumptions might be valid, for example, in cardiac blood-pool imaging or in transmission tomography of the thorax for non-uniform attenuation correction of emission tomography. In the former imaging situation, the intensities or radionuclide activities within the regions of myocardium, blood-pool and background may be relatively constant and the three activity levels can be distinct. For the latter case, the attenuation coefficients of bone, lungs and soft tissues can be determined prior to reconstructing the attenuation map. The contiguous image regions are expected to be simultaneously segmented during image reconstruction. We tested the image model with experimental phantom studies. The phantom consisted of a plastic cylinder having an elliptical cross section and containing five contiguous regions. There were three distinct activity levels within the phantom. Projection data were acquired using a SPECT system. Reconstructions were performed using an iterative maximum a posteriori probability procedure. As expected, the reconstructed image consisted of contiguous regions and the acitivities within the regions were relatively constant. Compared with maximum likelihood and a Bayesian approach using a Gibbs prior, the results obtained using the image model demonstrated the improvement in identifying the contiguous regions and the associated activities.

Quantitative SPECT imaging with indium-111

The potential of SPECT (single photon emission computed tomography) to quantify the distribution of indium-111 was investigated in an experimental phantom study. Nonuniform attenuation compensation using acquired transmission data was compared to uniform compensation based on reconstructed quantitative accuracy and noise. The reconstructed transmission data provided the attenuation map for the nonuniform compensation. Results showed that nonuniform attenuation compensation improved image quality, quantitative accuracy, and noise compared to uniform compensation. Noise increased with a decrease in counts in the nonuniform attenuation map but remained substantially below the uniform compensation level. The noise effect was observed with both Chang and ML-EM (maximum-likelihood expectation-maximization) reconstruction methods. Independent reconstruction of the 172- and 247-keV emission data was compared to the reconstruction of the combined 172- and 247-keV projection data. Improved quantitative accuracy and image noise resulted when both In-111 emission energies were used. However, independent reconstruction of the two energies did not substantially improve accuracy or noise compared with the reconstruction of the combined data. >

Three-dimensional photon detection kernels and their application to SPECT reconstruction

In single photon emission computed tomography (SPECT), three-dimensional photon detection kernels characterize the probabilities that photons emitted by radio-isotopes in different parts of the source region will be detected at particular projection pixels of the projection images. Monte Carlo modelling is used to study these kernels for the case of parallel hole collimators. The use of vectorized Monte Carlo computer code speeds the modelling computations. The contributions of direct and scattered photons to projection data in a transverse plane from neighbouring planes are significant for the case of uniform activity within a water-filled cylinder. A reconstruction method using the 3D kernels is proposed in which projection measurements in three adjacent planes are used simultaneously to estimate the source activity of the center plane. This multiple slice method accounts for the fact that photons detected in a given transverse plane may have originated in other transverse planes with different activity distributions. The matrix equations for image reconstruction are solved using generalized matrix inverses. The new method shows compensation for 3D photon detection effects when applied to projection data from a numerical simulation and a cardiac phantom experiment. Quantitation for the numerical study is improved compared with results from a single slice reconstruction method.