Role of Sparsity in High Dimensional Signal Detection and Estimation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Role of Sparsity in High Dimensional Signal Detection and Estimation write by Manqi Zhao. This book was released on 2011. Role of Sparsity in High Dimensional Signal Detection and Estimation available in PDF, EPUB and Kindle. Abstract: Processing high dimensional data arises in a number of real world applications such as financial data analysis, hyperspectral imagery, and video surveillance. The data are organized in a rectangular array with n rows and p columns, where the rows represent different measurements and the columns represent different features. High dimensional statistical inference studies signal detection and estimation problems in the scenario when n “ p . The main challenge of high dimensional statistical inference is the curse of dimensionality phenomena. The curse of dimensionality leads to intractability of accurately approximating high-dimensional density function. Nevertheless, data samples in many high dimensional problems come from an underlying low dimensional space or manifold. This limits the degrees of freedom (DOF) in the ambient space. This structure can be exploited for statistical inference. Another feature of high dimensional data is concentration of measure phenomena, which states that certain smooth random functions in high dimensional space are nearly constant. The philosophy is that under mild conditions it is easy to predict the behavior of high dimensional data.In this thesis, we exploit the DOF structure in detection and estimation of high dimensional data together with concentration of measure inequalities to obtain new results. In particular we consider the sparsity model for compressed sensing, the joint sparse and Markov structure for blind deconvolution, the manifold model for outlier detection and the temporally local anomaly structure for time-series anomaly detection. We present a linear programming solution for signal support recovery from noisy measurements that leverages sparse constraint. We simultaneously reconstruct the unknown autoregressive filter and the driving process in light of the joint structure on sparsity and Markov property. We develop novel non-parametric adaptive anomaly detection algorithm for high dimensional data that can adapt to local sparse manifold structure. We develop a clustering algorithm that accounts for highly unbalanced proximal and complex shaped clusters based on the scheme of reweighting the graph edge similarity. We propose a new paradigm for time-series anomaly detection that exploits the local anomaly structure. Our analysis in compressed sensing shows that the achievable bound in terms of SNR, the number of measurements, and admissible sparsity level of a linear programming solution matches the optimal information-theoretic in an order-wise sense. Our result in anomaly detection suggests that estimating high dimensional level-set can be avoided by computing a sufficient p-value statistic. The resulting anomaly detector is asymptotically uniformly most powerful against any uniformly mixing density. We also provide a generalization of this p-value statistic in time-series anomaly detection with false alarm control.
Sparse Representations for Radar with MATLAB® Examples
Sparse Representations for Radar with MATLAB® Examples - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Sparse Representations for Radar with MATLAB® Examples write by Peter Knee. This book was released on 2012-10-01. Sparse Representations for Radar with MATLAB® Examples available in PDF, EPUB and Kindle. Although the field of sparse representations is relatively new, research activities in academic and industrial research labs are already producing encouraging results. The sparse signal or parameter model motivated several researchers and practitioners to explore high complexity/wide bandwidth applications such as Digital TV, MRI processing, and certain defense applications. The potential signal processing advancements in this area may influence radar technologies. This book presents the basic mathematical concepts along with a number of useful MATLAB® examples to emphasize the practical implementations both inside and outside the radar field. Table of Contents: Radar Systems: A Signal Processing Perspective / Introduction to Sparse Representations / Dimensionality Reduction / Radar Signal Processing Fundamentals / Sparse Representations in Radar
Concentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference
Concentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Concentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference write by Zheng Gao. This book was released on 2021-09-07. Concentration of Maxima and Fundamental Limits in High-Dimensional Testing and Inference available in PDF, EPUB and Kindle. This book provides a unified exposition of some fundamental theoretical problems in high-dimensional statistics. It specifically considers the canonical problems of detection and support estimation for sparse signals observed with noise. Novel phase-transition results are obtained for the signal support estimation problem under a variety of statistical risks. Based on a surprising connection to a concentration of maxima probabilistic phenomenon, the authors obtain a complete characterization of the exact support recovery problem for thresholding estimators under dependent errors.
Study on Signal Detection and Recovery Methods with Joint Sparsity
Study on Signal Detection and Recovery Methods with Joint Sparsity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Study on Signal Detection and Recovery Methods with Joint Sparsity write by Xueqian Wang. This book was released on 2023-09-30. Study on Signal Detection and Recovery Methods with Joint Sparsity available in PDF, EPUB and Kindle. The task of signal detection is deciding whether signals of interest exist by using their observed data. Furthermore, signals are reconstructed or their key parameters are estimated from the observations in the task of signal recovery. Sparsity is a natural characteristic of most of signals in practice. The fact that multiple sparse signals share the common locations of dominant coefficients is called by joint sparsity. In the context of signal processing, joint sparsity model results in higher performance of signal detection and recovery. This book focuses on the task of detecting and reconstructing signals with joint sparsity. The main contents include key methods for detection of joint sparse signals and their corresponding theoretical performance analysis, and methods for joint sparse signal recovery and their application in the context of radar imaging.
Adaptive Methods and Theory for Sparse Signal Recovery
Adaptive Methods and Theory for Sparse Signal Recovery - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Adaptive Methods and Theory for Sparse Signal Recovery write by . This book was released on 2012. Adaptive Methods and Theory for Sparse Signal Recovery available in PDF, EPUB and Kindle. The study of sparsity has recently been given tremendous attention within the signal processing community. Sparsity is the simple notion that a high dimensional signal or vector can be well represented by a relatively small number of coefficients; sparse signals arise in communications, coding, remote sensing, imaging, biology, medicine, and many more. Adaptivity, the ability to change behavior based on input from the environment, has long been recognized by engineers as a means to improve performance. The focus of this thesis is development of adaptive measurement techniques and theory for sparse signal recovery problems. Surprisingly, adaptive measurement systems can drastically improve performance by reducing the signal noise ratio (SNR) needed for successful inference of a sparse signal. The first portion of this thesis comprises contributions to the study of multiple-testing and sparse recovery problems from the perspective of sequential analysis. We propose a simple yet powerful adaptive procedure termed Sequential Thresholding, which can succeed with a relatively small number of adaptive measurements. We develop the fundamental performance limits of adaptive testing in this setting, and prove the asymptotic optimality of Sequential Thresholding. We then transition to the field of compressive sensing. In this setting we develop an adaptive, compressive, search procedure that is provably optimal in terms of dependence on SNR for a certain class of sparse signals. The fourth chapter of this thesis focuses on a problem termed the search across multiple populations. Here, sparsity manifests itself as the rare occurrence of some `atypical' statistical population. A general theory is developed, with tight upper and lower bounds on the number of samples required to find such an atypical population. Instantiating the general theory results in the tightest known bounds for some well-studied problems. Lastly, this thesis focuses on the problem of non-coherent signal detection in multipath fading channels. Here, the signaling duration and bandwidth of the transmit signal are adapted to exploit the statistical behavior of the wireless environment. Sparsity arises as bandwidth and signaling duration become large.
