Coherence: In Signal Processing and Machine Learning

This book provides a comprehensive framework for signal processing and machine learning, organizing principles and methods into coherence. It covers inference, dimension reduction, detection, estimation, and uncertainty quantification, with applications in communications, cognitive radio, radar, and imaging. The appendices provide a matrix theory account, SVD, multivariate normal distribution, and coherence statistics.

Format: Hardback
Length: 487 pages
Publication date: 02 January 2023
Publisher: Springer International Publishing AG

This comprehensive book delves into the realm of signal processing and machine learning, seamlessly integrating principles and methodologies within the framework of coherence. It presents a wealth of classical and modern inference techniques, many of which are unveiled for the first time in this publication. General results derived from these methods find applications in diverse fields such as communications, cognitive radio, passive and active radar and sonar, multi-sensor array processing, spectrum analysis, hyperspectral imaging, subspace clustering, and related areas.

The reader will encounter groundbreaking findings in model fitting, dimension reduction, detection, estimation, space-time series analysis, subspace averaging, and uncertainty quantification. Throughout, the transformation invariances of statistics are elucidated, geometries are illuminated, and null distributions are provided when tractable. Stochastic representations receive particular emphasis, as they are essential for conducting Monte Carlo simulations.

The appendices offer a comprehensive account of matrix theory, the Singular Value Decomposition (SVD), the multivariate normal distribution, and numerous distributions pertinent to coherence statistics. The book commences with a review of classical results in the physical and engineering sciences, where coherence assumes a pivotal role. Subsequently, least squares theory and the theory of minimum mean-squared error estimation are established, with a particular focus on statistics that can be interpreted as coherence statistics. A chapter on classical hypothesis tests for covariance structure introduces the subsequent three chapters on matched and adaptive subspace detectors. These detectors are derived from likelihood reasoning, yet their geometries and invariances render them as coherence statistics. A chapter on independence testing in space-time data sets culminates in the definition of broadband coherency.

In summary, this book serves as a valuable resource for researchers and practitioners seeking to harness the power of coherence in signal processing and machine learning. It provides a comprehensive exploration of principles, methods, and applications, enabling readers to advance their understanding and develop innovative solutions in a wide range of scientific and technological domains.

Weight: 928g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031133305
Edition number: 1st ed. 2022