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.

Neuromorphic model for sound source segregation

While humans can easily segregate and track a speaker's voice in a loud noisy environment, most modern speech recognition systems still perform poorly in loud background noise. The computational principles behind auditory source segregation in humans is not yet fully understood. In this dissertation, we develop a computational model for source segregation inspired by auditory processing in the brain. To support the key principles behind the computational model, we conduct a series of electro-encephalography experiments using both simple tone-based stimuli and more natural speech stimulus. Most source segregation algorithms utilize some form of prior information about the target speaker or use more than one simultaneous recording of the noisy speech mixtures. Other methods develop models on the noise characteristics. Source segregation of simultaneous speech mixtures with a single microphone recording and no knowledge of the target speaker is still a challenge. Using the principle of temporal coherence, we develop a novel computational model that exploits the difference in the temporal evolution of features that belong to different sources to perform unsupervised monaural source segregation. While using no prior information about the target speaker, this method can gracefully incorporate knowledge about the target speaker to further enhance the segregation.Through a series of EEG experiments we collect neurological evidence to support the principle behind the model. Aside from its unusual structure and computational innovations, the proposed model provides testable hypotheses of the physiological mechanisms of the remarkable perceptual ability of humans to segregate acoustic sources, and of its psychophysical manifestations in navigating complex sensory environments. Results from EEG experiments provide further insights into the assumptions behind the model and provide motivation for future single unit studies that can provide more direct evidence for the principle of temporal coherence.