In view of the significance of the array manifold in array processing and array communications, the role of differential geometry as an analytical tool cannot be overemphasized. Differential geometry is mainly confined to the investigation of the geometric properties of manifolds in three-dimensional Euclidean space R3 and in real spaces of higher dimension.Extending the theoretical framework to complex spaces, this invaluable book presents a summary of those results of differential geometry which are of practical interest in the study of linear, planar and three-dimensional array geometries.
Geometry processing, or mesh processing, is a fast-growing area of research that uses concepts from applied mathematics, computer science, and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation, and transmission of complex 3D models. Applications of geometry processing algorithms already cover a wide range of areas from multimedia, entertainment, and classical computer-aided design, to biomedical computing, reverse engineering, and scientific computing. Over the last several years, triangle meshes have become increasingly popular, as irregular triangle meshes have developed into a valuable alternative to traditional spline surfaces. This book discusses the whole geometry processing pipeline based on triangle meshes. The pipeline starts with data input, for example, a model acquired by 3D scanning techniques. This data can then go through processes of error removal, mesh creation, smoothing, conversion, morphing, and more. The authors detail techniques for those processes using triangle meshes. A supplemental website contains downloads and additional information.
The NATO Advanced Research Workshop on Issues in Acoustic Signal/Image Processing and Recognition was held August 5-9, 1982 at the Cappuccini complex in San Miniato Italy. The Workshop was primarily concerned with the underwater acoustic signal processing and seismic signal analysis and a major effort was made to link these topics with pattern recognition, i~ge processing and artificial intelligence. Major issues and new approaches in these interrelated areas were closely examined in the Workshop. In addition to paper presentations three discussion sessions were held on! (1) spectral analysis in underwater acoustics, (2) seismic wave propaga tion, seismic imaging and migration, and seismic inversion, and (3) unresolved issues and future directions. This Proceedings volume includes most presentations made at the Workshop. The publication, like the meeting itself, is unique in the sense that it provides exten sive interactions among the closely related areas stated above. Such interactions which usually result in the integration of different systems or approaches are certainly much needed to achieve some performance breakthrough while individual systems or approaches reach their performance limit. I am grateful to all participants for their active participation that makes the Workshop very productive, and to Dr. Lewis J. Lloyd and Dr. Ralph Goodman for their help to arrange an informative visit to the SACLANT ASW Research Centre for the Workshop participants. I am confident that this publication will be equally produc tive to report important current research results and near-future research activity particularly in underwater acoustic signal processing.
Audio Signal Processing for Next-Generation Multimedia Communication Systems presents cutting-edge digital signal processing theory and implementation techniques for problems including speech acquisition and enhancement using microphone arrays, new adaptive filtering algorithms, multichannel acoustic echo cancellation, sound source tracking and separation, audio coding, and realistic sound stage reproduction. This book's focus is almost exclusively on the processing, transmission, and presentation of audio and acoustic signals in multimedia communications for telecollaboration where immersive acoustics will play a great role in the near future.
Brings together in one book classical and modern DOA techniques, showing the connections between them. Contains contributions from the leading people in the field. Gives a concise and easy- to- read introduction to the classical techniques Evaluates the strengths and weaknesses of key super-resolution techniques. Includes applications to sensor networks Classical and Modern Direction of Arrival Estimation, contains both theory and practice of direction finding by the leading researchers in the field. This unique blend of ...
Many problems in the sciences and engineering can be rephrased as optimization problems on matrix search spaces endowed with a so-called manifold structure. This book shows how to exploit the special structure of such problems to develop efficient numerical algorithms. It places careful emphasis on both the numerical formulation of the algorithm and its differential geometric abstraction--illustrating how good algorithms draw equally from the insights of differential geometry, optimization, and numerical analysis. Two more theoretical chapters provide readers with the background in differential geometry necessary to algorithmic development. In the other chapters, several well-known optimization methods such as steepest descent and conjugate gradients are generalized to abstract manifolds. The book provides a generic development of each of these methods, building upon the material of the geometric chapters. It then guides readers through the calculations that turn these geometrically formulated methods into concrete numerical algorithms. The state-of-the-art algorithms given as examples are competitive with the best existing algorithms for a selection of eigenspace problems in numerical linear algebra. Optimization Algorithms on Matrix Manifolds offers techniques with broad applications in linear algebra, signal processing, data mining, computer vision, and statistical analysis. It can serve as a graduate-level textbook and will be of interest to applied mathematicians, engineers, and computer scientists.
This book gives an introduction to fiber spaces and differential operators on smooth manifolds. Over the last 20 years, the authors developed an algebraic approach to the subject and they explain in this book why differential calculus on manifolds can be considered as an aspect of commutative algebra. This new approach is based on the fundamental notion of observable which is used by physicists and will further the understanding of the mathematics underlying quantum field theory.
This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.
This work contains the proceedings of the Sensor Array and Multichannel Workshop held in the year 2000. It should be useful to researchers, professors, practitioners, students and professionals.
