Anomaly Detection in Noisy Images

Finding rare events in multidimensional data is an important detection problem that has applications in many fields, such as risk estimation in insurance industry, finance, flood prediction, medical diagnosis, quality assurance, security, or safety in transportation. The occurrence of such anomalies is so infrequent that there is usually not enough training data to learn an accurate statistical model of the anomaly class. In some cases, such events may have never been observed, so the only information that is available is a set of normal samples and an assumed pairwise similarity function. Such metric may only be known up to a certain number of unspecified parameters, which would either need to be learned from training data, or fixed by a domain expert. Sometimes, the anomalous condition may be formulated algebraically, such as a measure exceeding a predefined threshold, but nuisance variables may complicate the estimation of such a measure. Change detection methods used in time series analysis are not easily extendable to the multidimensional case, where discontinuities are not localized to a single point. On the other hand, in higher dimensions, data exhibits more complex interdependencies, and there is redundancy that could be exploited to adaptively model the normal data. In the first part of this dissertation, we review the theoretical framework for anomaly detection in images and previous anomaly detection work done in the context of crack detection and detection of anomalous components in railway tracks. In the second part, we propose new anomaly detection algorithms. The fact that curvilinear discontinuities in images are sparse with respect to the frame of shearlets, allows us to pose this anomaly detection problem as basis pursuit optimization. Therefore, we pose the problem of detecting curvilinear anomalies in noisy textured images as a blind source separation problem under sparsity constraints, and propose an iterative shrinkage algorithm to solve it. Taking advantage of the parallel nature of this algorithm, we describe how this method can be accelerated using graphical processing units (GPU). Then, we propose a new method for finding defective components on railway tracks using cameras mounted on a train. We describe how to extract features and use a combination of classifiers to solve this problem. Then, we scale anomaly detection to bigger datasets with complex interdependencies. We show that the anomaly detection problem naturally fits in the multitask learning framework. The first task consists of learning a compact representation of the good samples, while the second task consists of learning the anomaly detector. Using deep convolutional neural networks, we show that it is possible to train a deep model with a limited number of anomalous examples. In sequential detection problems, the presence of time-variant nuisance parameters affect the detection performance. In the last part of this dissertation, we present a method for adaptively estimating the threshold of sequential detectors using Extreme Value Theory on a Bayesian framework. Finally, conclusions on the results obtained are provided, followed by a discussion of possible future work.

THE RELATIVE SIGNIFICANCE OF SYNTACTIC KNOWLEDGE AND VOCABULARY KNOWLEDGE IN SECOND LANGUAGE LISTENING COMPREHENSION

The main purpose of the current study was to examine the role of vocabulary knowledge (VK) and syntactic knowledge (SK) in L2 listening comprehension, as well as their relative significance. Unlike previous studies, the current project employed assessment tasks to measure aural and proceduralized VK and SK. In terms of VK, to avoid under-representing the construct, measures of both breadth (VB) and depth (VD) were included. Additionally, the current study examined the role of VK and SK by accounting for individual differences in two important cognitive factors in L2 listening: metacognitive knowledge (MK) and working memory (WM). Also, to explore the role of VK and SK more fully, the current study accounted for the negative impact of anxiety on WM and L2 listening. The study was carried out in an English as a Foreign Language (EFL) context, and participants were 263 Iranian learners at a wide range of English proficiency from lower-intermediate to advanced. Participants took a battery of ten linguistic, cognitive and affective measures. Then, the collected data were subjected to several preliminary analyses, but structural equation modeling (SEM) was then used as the primary analysis method to answer the study research questions. Results of the preliminary analyses revealed that MK and WM were significant predictors of L2 listening ability; thus, they were kept in the main SEM analyses. The significant role of WM was only observed when the negative effect of anxiety on WM was accounted for. Preliminary analyses also showed that VB and VD were not distinct measures of VK. However, the results also showed that if VB and VD were considered separate, VD was a better predictor of L2 listening success. The main analyses of the current study revealed a significant role for both VK and SK in explaining success in L2 listening comprehension, which differs from findings from previous empirical studies. However, SEM analysis did not reveal a statistically significant difference in terms of the predictive power of the two linguistic factors. Descriptive results of the SEM analysis, along with results from regression analysis, indicated to a more significant role for VK.