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Author: Jurij I. Ingster
Publisher:
ISBN:
Category :
Languages : en
Pages : 53
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Book Description
Author: Jurij I. Ingster
Publisher:
ISBN:
Category :
Languages : en
Pages : 53
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Book Description
Author: Manqi Zhao
Publisher:
ISBN:
Category :
Languages : en
Pages : 414
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Book Description
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.
Author: Zeyu Wang
Publisher: CRC Press
ISBN: 1040030424
Category : Technology & Engineering
Languages : en
Pages : 195
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Book Description
This book systematically presents adaptive multichannel signal detection in three types of non-ideal environments, including sample-starved scenarios, signal mismatch scenarios, and noise plus subspace interference environments. The authors provide definitions of key concepts, detailed derivations of adaptive multichannel signal detectors, and specific examples for each non-ideal environment. In addition, the possible future trend of adaptive detection methods is discussed, as well as two further research points – namely, the adaptive detection algorithms based on information geometry, and the hybrid approaches that combine adaptive detection algorithms with machine learning algorithms. The book will be of interest to researchers, advanced undergraduates, and graduate students in sonar, radar signal processing, and communications engineering.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 346
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Book Description
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.
Author: Eric Edward Anderson
Publisher:
ISBN:
Category : Signal detection
Languages : en
Pages : 224
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Author: Mengxi Yi
Publisher: Springer Nature
ISBN: 3031226879
Category : Mathematics
Languages : en
Pages : 500
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Book Description
This book presents recent developments in multivariate and robust statistical methods. Featuring contributions by leading experts in the field it covers various topics, including multivariate and high-dimensional methods, time series, graphical models, robust estimation, supervised learning and normal extremes. It will appeal to statistics and data science researchers, PhD students and practitioners who are interested in modern multivariate and robust statistics. The book is dedicated to David E. Tyler on the occasion of his pending retirement and also includes a review contribution on the popular Tyler’s shape matrix.
Author: Yuanwei Jin
Publisher:
ISBN:
Category :
Languages : en
Pages : 372
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Author: Thomas G. Kincaid
Publisher:
ISBN:
Category :
Languages : en
Pages : 31
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Book Description
The report proposes a design of an adaptive receiver for the detection and estimation of nearly periodic signals in additive Gaussian noise. A nearly periodic signal is defined to be a sample function of a Gaussian random process which can be divided into equal length intervals, called periods, in such a manner that the correlation between periods decreases exponentially with their separation. The receiver computes a low signal-to-noise ratio conditional likelihood ratio from which the observer must make decisions. The likelihood ratio is conditional because the receiver estimates any unknown parameters necessary for the computation of the true likelihood ratio. Thus the receiver can only compute a likelihood ratio conditioned upon these estimates being the true values of the unknown parameters. The receiver consists of pre-emphasis filters followed by a comb filter, energy detector, and weighted summation. A theoretical evaluation of the receiver, in terms of ROC curves, is made for the special case of nearly periodic signals with statistically independent equal-strength harmonics in white noise of known power. (Author).
Author: Ashish Ghosh
Publisher: Springer
ISBN: 3540770461
Category : Computers
Languages : en
Pages : 693
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Book Description
This book constitutes the refereed proceedings of the Second International Conference on Pattern Recognition and Machine Intelligence, PReMI 2007, held in Kolkata, India in December 2007. The papers are organized in topical sections on pattern recognition, image analysis, soft computing and applications, data mining and knowledge discovery, bioinformatics, signal and speech processing, document analysis and text mining, biometrics, and video analysis.
Author: Saurabh Prasad
Publisher: Springer Nature
ISBN: 3030386171
Category : Computers
Languages : en
Pages : 464
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Book Description
This book reviews the state of the art in algorithmic approaches addressing the practical challenges that arise with hyperspectral image analysis tasks, with a focus on emerging trends in machine learning and image processing/understanding. It presents advances in deep learning, multiple instance learning, sparse representation based learning, low-dimensional manifold models, anomalous change detection, target recognition, sensor fusion and super-resolution for robust multispectral and hyperspectral image understanding. It presents research from leading international experts who have made foundational contributions in these areas. The book covers a diverse array of applications of multispectral/hyperspectral imagery in the context of these algorithms, including remote sensing, face recognition and biomedicine. This book would be particularly beneficial to graduate students and researchers who are taking advanced courses in (or are working in) the areas of image analysis, machine learning and remote sensing with multi-channel optical imagery. Researchers and professionals in academia and industry working in areas such as electrical engineering, civil and environmental engineering, geosciences and biomedical image processing, who work with multi-channel optical data will find this book useful.
