We describe a nonparametric framework for incorporating information from co-registered anatomical images into positron emission tomographic (PET) image reconstruction through priors based on information theoretic similarity measures. We compare and evaluate the use of mutual information (MI) and joint entropy (JE) between feature vectors extracted from the anatomical and PET images as priors in PET reconstruction. Scale-space theory provides a framework for the analysis of images at different levels of detail, and we use this approach to define feature vectors that emphasize prominent boundaries in the anatomical and functional images, and attach less importance to detail and noise that is less likely to be correlated in the two images. Through simulations that model the best case scenario of perfect agreement between the anatomical and functional images, and a more realistic situation with a real magnetic resonance image and a PET phantom that has partial volumes and a smooth variation of intensities, we evaluate the performance of MI and JE based priors in comparison to a Gaussian quadratic prior, which does not use any anatomical information. We also apply this method to clinical brain scan data using F18 Fallypride, a tracer that binds to dopamine receptors and therefore localizes mainly in the striatum. We present an efficient method of computing these priors and their derivatives based on fast Fourier transforms that reduce the complexity of their convolution-like expressions. Our results indicate that while sensitive to initialization and choice of hyperparameters, information theoretic priors can reconstruct images with higher contrast and superior quantitation than quadratic priors.
Diffuse optical tomography (DOT) retrieves the spatially distributed optical characteristics of a medium from external measurements. Recovering these parameters of interest involves solving a non-linear and severely ill-posed inverse problem. In this thesis we propose methods towards the regularization of DOT via the introduction of spatially unregistered, a priori information from alternative high resolution anatomical modalities, using the information theory concepts of joint entropy (JE) and mutual information (MI). Such functionals evaluate the similarity between the reconstructed optical image and the prior image, while bypassing the multi-modality barrier manifested as the incommensurate relation between the gray value representations of corresponding anatomical features in the modalities involved. By introducing structural a priori information in the image reconstruction process, we aim to improve the spatial resolution and quantitative accuracy of the solution.A further condition for the accurate incorporation of a priori information is the establishment of correct alignment between the prior image and the probed anatomy in a common coordinate system. However, limited information regarding the probed anatomy is known prior to the reconstruction process.In this work we explore the potentiality of spatially registering the prior image simultaneously with the solution of the reconstruction process.We provide a thorough explanation of the theory from an imaging perspective, accompanied by preliminary results obtained by numerical simulations as well as experimental data. In addition we compare the performance of MI and JE. Finally, we propose a method for fast joint entropy evaluation and optimization, which we later employ for the information theoretic regularization of DOT. The main areas involved in this thesis are: inverse problems, image reconstruction & regularization, diffuse optical tomography and medical image registration. Statement of intellectual contributionI, Christos Panagiotou, declare that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been properly indicated in the thesis.
Abstract-In this paper, we address the problem of detecting the presence of myocardial scar from standard ECG/VCG recordings, giving effort to develop a screening system for the early detection of scar in the point-of-care. Based on the pathophysiological implications of scarred myocardium, which results in disordered electrical conduction, we have implemented four distinct ECG signal processing methodologies in order to obtain a set of features that can capture the presence of myocardial scar. Two of these methodologies: a.) the use of a template ECG heartbeat, from records with scar absence coupled with Wavelet coherence analysis and b.) the utilization of the VCG are novel approaches for detecting scar presence. Following, the pool of extracted features is utilized to formulate an SVM classification model through supervised learning. Feature selection is also employed to remove redundant features and maximize the classifier's performance. Classification experiments using 260 records from three different databases reveal that the proposed system achieves 89.22% accuracy when applying 10-fold cross validation, and 82.07% success rate when testing it on databases with different inherent characteristics with similar levels of sensitivity (76%) and specificity (87.5%).
We present reverberation mapping measurements for the prominent ultraviolet broad emission lines of the active galactic nucleus Mrk 817 using 165 spectra obtained with the Cosmic Origins Spectrograph on the Hubble Space Telescope. Our ultraviolet observations are accompanied by X-ray, optical, and near-infrared observations as part of the AGN Space Telescope and Optical Reverberation Mapping Program 2 (AGN STORM 2). Using the cross-correlation lag analysis method, we find significant correlated variations in the continuum and emission-line light curves. We measure rest-frame delayed responses between the far-ultraviolet continuum at 1180 Å and Lyα λ1215 Å ( 10.4 − 1.4 + 1.6 days), N v λ1240 Å ( 15.5 − 4.8 + 1.0 days), Si iv + ]O iv λ1397 Å ( 8.2 − 1.4 + 1.4 days), C iv λ1549 Å ( 11.8 − 2.8 + 3.0 days), and He ii λ1640 Å ( 9.0 − 1.9 + 4.5 days) using segments of the emission-line profile that are unaffected by absorption and blending, which results in sampling different velocity ranges for each line. However, we find that the emission-line responses to continuum variations are more complex than a simple smoothed, shifted, and scaled version of the continuum light curve. We also measure velocity-resolved lags for the Lyα and C iv emission lines. The lag profile in the blue wing of Lyα is consistent with virial motion, with longer lags dominating at lower velocities, and shorter lags at higher velocities. The C iv lag profile shows the signature of a thick rotating disk, with the shortest lags in the wings, local peaks at ±1500 km s−1, and a local minimum at the line center. The other emission lines are dominated by broad absorption lines and blending with adjacent emission lines. These require detailed models, and will be presented in future work.
In emission tomography (ET), fast developing Bayesian reconstruction methods can incorporate anatomical information derived from co-registered scanning modalities, such as magnetic resonance (MR) and computed tomography (CT). We propose a Bayesian image reconstruction method for single photon emission computed tomography (SPECT), using a joint entropy (JE) similarity measure to embed MR anatomical data. An optimized non-parametric Parzen window approach is used for fast and efficient estimation of the probability density function (PDF) of the JE metric. It is known that the quality of the Parzen estimates strongly depends on the kernel bandwidth of the smoothing function. When the density is over or under-smoothed, because of too large or small bandwidth value, this leads to an incorrect entropy estimate and, eventually, to a biased solution.To alleviate the problem of searching manually for the most suitable weight for the smoothing function and the number of bins for the histogram, we use an adaptive method to find these parameters automatically from the data on each iteration of the Bayesian algorithm. We assess the NRMSE-variance behaviour of the MAP-EM reconstruction method in relation to the quality of the PDF building. For the different bandwidth values of the Gaussian kernel for the density function, an emission image is reconstructed using MR data as a prior. Preliminary numerical experiments are performed using simulated co-registered 2D and 3D SPECT/MR data. Comparison of proposed technique with neighbourhood dependent anatomically-based prior is presented. Lesions are simulated to be apparent on the gray matter of the 3D SPECT data, but invisible on MRI. Preliminary results demonstrate that applying optimal density estimation for JE metric is feasible and more efficient compared to non-adaptive techniques.
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