Compressed Sensing For Functional Magnetic Resonance Imaging Data

This thesis addresses the possibility of applying the compressed sensing (CS) framework to Functional Magnetic Resonance Imaging (fMRI) acquisition. The fMRI is one of the non-invasive neuroimaging technique that allows the brain activity to be captured and analysed in a living body. One disadvantage of fMRI is the trade-off between the spatial and temporal resolution of the data. To keep the experiments within a reasonable length of time, the current acquisition technique sacrifices the spatial resolution in favour of the temporal resolution. It is possible to improve this trade-off using compressed sensing. The main contribution of this thesis is to propose a novel reconstruction method, named Referenced Compressed Sensing, which exploits the redundancy between a signal and a correlated reference by using their distance as an objective function. The compressed video sequences reconstructed using Referenced CS have at least 50% higher in terms of Peak Signal-to-Noise Ratio (PSNR) compared to state-of-the-art conventional reconstruction methods. This thesis also addresses two issues related to Referenced CS. Firstly, the relationship between the reference and the reconstruction performance is studied. To maintain the high-quality references, the Running Gaussian Average (RGA) reference estimator is proposed. The reconstructed results have at least 3dB better PSNR performance with the use of RGA references. Secondly, the Referenced CS with Least Squares is proposed. This study shows that by incorporating the correlated reference, it is possible to perform a linear reconstruction as opposed to the iterative reconstruction commonly used in CS. This approach gives at least 19% improvement in PSNR compared to the state of the art, while reduces the computation time by at most 1200 times. The proposed method is applied to the fMRI data. This study shows that, using the same amount of samples, the data reconstructed using Referenced CS has higher resolution than the conventional acquisition technique and has on average 50% higher PSNR than state-of-the-art reconstructions. Lastly, to enhance the feature of interest in the fMRI data, the baseline independent (BI) analysis is proposed. Using the BI analysis shows up to 25% improvement in the accuracy of the Referenced CS feature

Concentration of measure, negative association, and machine learning

In this thesis we consider concentration inequalities and the concentration of measure phenomenon from a variety of angles. Sharp tail bounds on the deviation of Lipschitz functions of independent random variables about their mean are well known. We consider variations on this theme for dependent variables on the Boolean cube. In recent years negatively associated probability distributions have been studied as potential generalizations of independent random variables. Results on this class of distributions have been sparse at best, even when restricting to the Boolean cube. We consider the class of negatively associated distributions topologically, as a subset of the general class of probability measures. Both the weak (distributional) topology and the total variation topology are considered, and the simpler notion of negative correlation is investigated. The concentration of measure phenomenon began with Milman's proof of Dvoretzky's theorem, and is therefore intimately connected to the field of high-dimensional convex geometry. Recently this field has found application in the area of compressed sensing. We consider these applications and in particular analyze the use of Gordon's min-max inequality in various compressed sensing frameworks, including the Dantzig selector and the matrix uncertainty selector. Finally we consider the use of concentration inequalities in developing a theoretically sound anomaly detection algorithm. Our method uses a ranking procedure based on KNN graphs of given data. We develop a max-margin learning-to-rank framework to train limited complexity models to imitate these KNN scores. The resulting anomaly detector is shown to be asymptotically optimal in that for any false alarm rate α, its decision region converges to the α-percentile minimum volume level set of the unknown underlying density

Recent Advances in Signal Processing

The signal processing task is a very critical issue in the majority of new technological inventions and challenges in a variety of applications in both science and engineering fields. Classical signal processing techniques have largely worked with mathematical models that are linear, local, stationary, and Gaussian. They have always favored closed-form tractability over real-world accuracy. These constraints were imposed by the lack of powerful computing tools. During the last few decades, signal processing theories, developments, and applications have matured rapidly and now include tools from many areas of mathematics, computer science, physics, and engineering. This book is targeted primarily toward both students and researchers who want to be exposed to a wide variety of signal processing techniques and algorithms. It includes 27 chapters that can be categorized into five different areas depending on the application at hand. These five categories are ordered to address image processing, speech processing, communication systems, time-series analysis, and educational packages respectively. The book has the advantage of providing a collection of applications that are completely independent and self-contained; thus, the interested reader can choose any chapter and skip to another without losing continuity

Efficient and Robust Methods for Audio and Video Signal Analysis

This thesis presents my research concerning audio and video signal processing and machine learning. Specifically, the topics of my research include computationally efficient classifier compounds, automatic speech recognition (ASR), music dereverberation, video cut point detection and video classification.Computational efficacy of information retrieval based on multiple measurement modalities has been considered in this thesis. Specifically, a cascade processing framework, including a training algorithm to set its parameters has been developed for combining multiple detectors or binary classifiers in computationally efficient way. The developed cascade processing framework has been applied on video information retrieval tasks of video cut point detection and video classification. The results in video classification, compared to others found in the literature, indicate that the developed framework is capable of both accurate and computationally efficient classification. The idea of cascade processing has been additionally adapted for the ASR task. A procedure for combining multiple speech state likelihood estimation methods within an ASR framework in cascaded manner has been developed. The results obtained clearly show that without impairing the transcription accuracy the computational load of ASR can be reduced using the cascaded speech state likelihood estimation process.Additionally, this thesis presents my work on noise robustness of ASR using a nonnegative matrix factorization (NMF) -based approach. Specifically, methods for transformation of sparse NMF-features into speech state likelihoods has been explored. The results reveal that learned transformations from NMF activations to speech state likelihoods provide better ASR transcription accuracy than dictionary label -based transformations. The results, compared to others in a noisy speech recognition -challenge show that NMF-based processing is an efficient strategy for noise robustness in ASR.The thesis also presents my work on audio signal enhancement, specifically, on removing the detrimental effect of reverberation from music audio. In the work, a linear prediction -based dereverberation algorithm, which has originally been developed for speech signal enhancement, was applied for music. The results obtained show that the algorithm performs well in conjunction with music signals and indicate that dynamic compression of music does not impair the dereverberation performance