Probabilistic modeling of wavelet coefficients for processing of image and video signals

Statistical estimation and detection techniques are widely used in signal processing including wavelet-based image and video processing. The probability density function (PDF) of the wavelet coefficients of image and video signals plays a key role in the development of techniques for such a processing. Due to the fixed number of parameters, the conventional PDFs for the estimators and detectors usually ignore higher-order moments. Consequently, estimators and detectors designed using such PDFs do not provide a satisfactory performance. This thesis is concerned with first developing a probabilistic model that is capable of incorporating an appropriate number of parameters that depend on higher-order moments of the wavelet coefficients. This model is then used as the prior to propose certain estimation and detection techniques for denoising and watermarking of image and video signals. Towards developing the probabilistic model, the Gauss-Hermite series expansion is chosen, since the wavelet coefficients have non-compact support and their empirical density function shows a resemblance to the standard Gaussian function. A modification is introduced in the series expansion so that only a finite number of terms can be used for modeling the wavelet coefficients with rendering the resulting PDF to become negative. The parameters of the resulting PDF, called the modified Gauss-Hermite (NIGH) PDF, are evaluated in terms of the higher-order sample-moments. It is shown that the MGH PDF fits the empirical density function better than the existing PDFs that use a limited number of parameters do. The proposed MGH PDF is used as the prior of image and video signals in designing maximum a posteriori and minimum mean squared error-based estimators for denoising of image and video signals and log-likelihood ratio-based detector for watermarking of image signals. The performance of the estimation and detection techniques are then evaluated in terms of the commonly used metrics. It is shown through extensive experimentations that the estimation and detection techniques developed utilizing the proposed MGH PDF perform substantially better than those that utilize the conventional PDFs. These results confirm that the superior fit of the MGH PDF to the empirical density function resulting from the flexibility of the MGH PDF in choosing the number of parameters, which are functions of higher-order moments of data, leads to the better performance. Thus, the proposed MGH PDF should play a significant role in wavelet-based image and video signal processin

A generic framework for context-dependent fusion with application to landmine detection.

For complex detection and classification problems, involving data with large intra-class variations and noisy inputs, no single source of information can provide a satisfactory solution. As a result, combination of multiple classifiers is playing an increasing role in solving these complex pattern recognition problems, and has proven to be a viable alternative to using a single classifier. Over the past few years, a variety of schemes have been proposed for combining multiple classifiers. Most of these were global as they assign a degree of worthiness to each classifier, that is averaged over the entire training data. This may not be the optimal way to combine the different experts since the behavior of each one may not be uniform over the different regions of the feature space. To overcome this issue, few local methods have been proposed in the last few years. Local fusion methods aim to adapt the classifiers\u27 worthiness to different regions of the feature space. First, they partition the input samples. Then, they identify the best classifier for each partition and designate it as the expert for that partition. Unfortunately, current local methods are either computationally expensive and/or perform these two tasks independently of each other. However, feature space partition and algorithm selection are not independent and their optimization should be simultaneous. In this dissertation, we introduce a new local fusion approach, called Context Extraction for Local Fusion (CELF). CELF was designed to adapt the fusion to different regions of the feature space. It takes advantage of the strength of the different experts and overcome their limitations. First, we describe the baseline CELF algorithm. We formulate a novel objective function that combines context identification and multi-algorithm fusion criteria into a joint objective function. The context identification component thrives to partition the input feature space into different clusters (called contexts), while the fusion component thrives to learn the optimal fusion parameters within each cluster. Second, we propose several variations of CELF to deal with different applications scenario. In particular, we propose an extension that includes a feature discrimination component (CELF-FD). This version is advantageous when dealing with high dimensional feature spaces and/or when the number of features extracted by the individual algorithms varies significantly. CELF-CA is another extension of CELF that adds a regularization term to the objective function to introduce competition among the clusters and to find the optimal number of clusters in an unsupervised way. CELF-CA starts by partitioning the data into a large number of small clusters. As the algorithm progresses, adjacent clusters compete for data points, and clusters that lose the competition gradually become depleted and vanish. Third, we propose CELF-M that generalizes CELF to support multiple classes data sets. The baseline CELF and its extensions were formulated to use linear aggregation to combine the output of the different algorithms within each context. For some applications, this can be too restrictive and non-linear fusion may be needed. To address this potential drawback, we propose two other variations of CELF that use non-linear aggregation. The first one is based on Neural Networks (CELF-NN) and the second one is based on Fuzzy Integrals (CELF-FI). The latter one has the desirable property of assigning weights to subsets of classifiers to take into account the interaction between them. To test a new signature using CELF (or its variants), each algorithm would extract its set of features and assigns a confidence value. Then, the features are used to identify the best context, and the fusion parameters of this context are used to fuse the individual confidence values. For each variation of CELF, we formulate an objective function, derive the necessary conditions to optimize it, and construct an iterative algorithm. Then we use examples to illustrate the behavior of the algorithm, compare it to global fusion, and highlight its advantages. We apply our proposed fusion methods to the problem of landmine detection. We use data collected using Ground Penetration Radar (GPR) and Wideband Electro -Magnetic Induction (WEMI) sensors. We show that CELF (and its variants) can identify meaningful and coherent contexts (e.g. mines of same type, mines buried at the same site, etc.) and that different expert algorithms can be identified for the different contexts. In addition to the land mine detection application, we apply our approaches to semantic video indexing, image database categorization, and phoneme recognition. In all applications, we compare the performance of CELF with standard fusion methods, and show that our approach outperforms all these methods

Ambiguity in asset pricing and portfolio choice: a review of the literature

A growing body of empirical evidence suggests that investors’ behavior is not well described by the traditional paradigm of (subjective) expected utility maximization under rational expectations. A literature has arisen that models agents whose choices are consistent with models that are less restrictive than the standard subjective expected utility framework. In this paper we conduct a survey of the existing literature that has explored the implications of decision-making under ambiguity for financial market outcomes, such as portfolio choice and equilibrium asset prices. We conclude that the ambiguity literature has led to a number of significant advances in our ability to rationalize empirical features of asset returns and portfolio decisions, such as the empirical failure of the two-fund separation theorem in portfolio decisions, the modest exposure to risky securities observed for a majority of investors, the home equity preference in international portfolio diversification, the excess volatility of asset returns, the equity premium and the risk-free rate puzzles, and the occurrence of trading break-downs.Capital assets pricing model ; Investments

A comparison of features for large population speaker identification

Bibliography: leaves 95-104.Speech recognition systems all have one criterion in common; they perform better in a controlled environment using clean speech. Though performance can be excellent, even exceeding human capabilities for clean speech, systems fail when presented with speech data from more realistic environments such as telephone channels. The differences using a recognizer in clean and noisy environments are extreme, and this causes one of the major obstacles in producing commercial recognition systems to be used in normal environments. It is the lack of performance of speaker recognition systems with telephone channels that this work addresses. The human auditory system is a speech recognizer with excellent performance, especially in noisy environments. Since humans perform well at ignoring noise more than any machine, auditory-based methods are the promising approaches since they attempt to model the working of the human auditory system. These methods have been shown to outperform more conventional signal processing schemes for speech recognition, speech coding, word-recognition and phone classification tasks. Since speaker identification has received lot of attention in speech processing because of its waiting real-world applications, it is attractive to evaluate the performance using auditory models as features. Firstly, this study rums at improving the results for speaker identification. The improvements were made through the use of parameterized feature-sets together with the application of cepstral mean removal for channel equalization. The study is further extended to compare an auditory-based model, the Ensemble Interval Histogram, with mel-scale features, which was shown to perform almost error-free in clean speech. The previous studies of Elli to be more robust to noise were conducted on speaker dependent, small population, isolated words and now are extended to speaker independent, larger population, continuous speech. This study investigates whether the Elli representation is more resistant to telephone noise than mel-cepstrum as was shown in the previous studies, when now for the first time, it is applied for speaker identification task using the state-of-the-art Gaussian mixture model system

A comparison of the CAR and DAGAR spatial random effects models with an application to diabetics rate estimation in Belgium

When hierarchically modelling an epidemiological phenomenon on a finite collection of sites in space, one must always take a latent spatial effect into account in order to capture the correlation structure that links the phenomenon to the territory. In this work, we compare two autoregressive spatial models that can be used for this purpose: the classical CAR model and the more recent DAGAR model. Differently from the former, the latter has a desirable property: its ρ parameter can be naturally interpreted as the average neighbor pair correlation and, in addition, this parameter can be directly estimated when the effect is modelled using a DAGAR rather than a CAR structure. As an application, we model the diabetics rate in Belgium in 2014 and show the adequacy of these models in predicting the response variable when no covariates are available

A Statistical Approach to the Alignment of fMRI Data

Multi-subject functional Magnetic Resonance Image studies are critical. The anatomical and functional structure varies across subjects, so the image alignment is necessary. We define a probabilistic model to describe functional alignment. Imposing a prior distribution, as the matrix Fisher Von Mises distribution, of the orthogonal transformation parameter, the anatomical information is embedded in the estimation of the parameters, i.e., penalizing the combination of spatially distant voxels. Real applications show an improvement in the classification and interpretability of the results compared to various functional alignment methods

Transportation Systems Analysis and Assessment

The transportation system is the backbone of any social and economic system, and is also a very complex system in which users, transport means, technologies, services, and infrastructures have to cooperate with each other to achieve common and unique goals.The aim of this book is to present a general overview on some of the main challenges that transportation planners and decision makers are faced with. The book addresses different topics that range from user's behavior to travel demand simulation, from supply chain to the railway infrastructure capacity, from traffic safety issues to Life Cycle Assessment, and to strategies to make the transportation system more sustainable

Automatic analysis of malaria infected red blood cell digitized microscope images

Malaria is one of the three most serious diseases worldwide, affecting millions each year, mainly in the tropics where the most serious illnesses are caused by Plasmodium falciparum. This thesis is concerned with the automatic analysis of images of microscope slides of Giemsa stained thin-films of such malaria infected blood so as to segment red-blood cells (RBCs) from the background plasma, to accurately and reliably count the cells, identify those that were infected with a parasite, and thus to determine the degree of infection or parasitemia. Unsupervised techniques were used throughout owing to the difficulty of obtaining large quantities of training data annotated by experts, in particular for total RBC counts. The first two aims were met by optimisation of Fisher discriminants. For RBC segmentation, a well-known iterative thresholding method due originally to Otsu (1979) was used for scalar features such as the image intensity and a novel extension of the algorithm developed for multi-dimensional, colour data. Performance of the algorithms was evaluated and compared via ROC analysis and their convergence properties studied. Ways of characterising the variability of the image data and, if necessary of mitigating it, were discussed in theory. The size distribution of the objects segmented in this way indicated that optimisation of a Fisher discriminant could be further used for classifying objects as small artefacts, singlet RBCs, doublets, or triplets etc. of adjoining cells provided optimisation was via a global search. Application of constraints on the relationships between the sizes of singlet and multiplet RBCs led to a number of tests that enabled clusters of cells to be reliably identified and accurate total RBC counts to be made. Development of an application to make such counts could be very useful both in research laboratories and in improving treatment of malaria. Unfortunately, the very small number of pixels belonging to parasite infections mean that it is difficult to segment parasite objects and thus to identify infected RBCs and to determine the parasitemia. Preliminary attempts to do so by similar, unsupervised means using Fischer discriminants, even when applied in a hierarchical manner, though suggestive that it may ultimately be possible to develop such a system remain on the evidence currently available, inconclusive. Appendices give details of material from old texts no longer easily accessible