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.

FRAMEWORK SYNTHESIS FOR SYMBOLIC EXECUTION OF EVENT-DRIVEN FRAMEWORKS

Symbolic execution is a powerful program analysis technique, but it is very challenging to apply to programs built using event-driven frameworks, such as Android. The main reason is that the framework code itself is too complex to symbolically execute. The standard solution is to manually create a framework model that is simpler and more amenable to symbolic execution. However, developing and maintaining such a model by hand is difficult and error-prone. We claim that we can leverage program synthesis to introduce a high-degree of automation to the process of framework modeling. To support this thesis, we present three pieces of work. First, we introduced SymDroid, a symbolic executor for Android. While Android apps are written in Java, they are compiled to Dalvik bytecode format. Instead of analyzing an app’s Java source, which may not be available, or decompiling from Dalvik back to Java, which requires significant engineering effort and introduces yet another source of potential bugs in an analysis, SymDroid works directly on Dalvik bytecode. Second, we introduced Pasket, a new system that takes a first step toward automatically generating Java framework models to support symbolic execution. Pasket takes as input the framework API and tutorial programs that exercise the framework. From these artifacts and Pasket's internal knowledge of design patterns, Pasket synthesizes an executable framework model by instantiating design patterns, such that the behavior of a synthesized model on the tutorial programs matches that of the original framework. Lastly, in order to scale program synthesis to framework models, we devised adaptive concretization, a novel program synthesis algorithm that combines the best of the two major synthesis strategies: symbolic search, i.e., using SAT or SMT solvers, and explicit search, e.g., stochastic enumeration of possible solutions. Adaptive concretization parallelizes multiple sub-synthesis problems by partially concretizing highly influential unknowns in the original synthesis problem. Thanks to adaptive concretization, Pasket can generate a large-scale model, e.g., thousands lines of code. In addition, we have used an Android model synthesized by Pasket and found that the model is sufficient to allow SymDroid to execute a range of apps.