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Advanced Radar Detection Schemes Under Mismatched Signal Models
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Book Synopsis Advanced Radar Detection Schemes Under Mismatched Signal Models by : Francesco Bandiera
Download or read book Advanced Radar Detection Schemes Under Mismatched Signal Models written by Francesco Bandiera and published by Springer Nature. This book was released on 2022-06-01 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adaptive detection of signals embedded in correlated Gaussian noise has been an active field of research in the last decades. This topic is important in many areas of signal processing such as, just to give some examples, radar, sonar, communications, and hyperspectral imaging. Most of the existing adaptive algorithms have been designed following the lead of the derivation of Kelly's detector which assumes perfect knowledge of the target steering vector. However, in realistic scenarios, mismatches are likely to occur due to both environmental and instrumental factors. When a mismatched signal is present in the data under test, conventional algorithms may suffer severe performance degradation. The presence of strong interferers in the cell under test makes the detection task even more challenging. An effective way to cope with this scenario relies on the use of "tunable" detectors, i.e., detectors capable of changing their directivity through the tuning of proper parameters. The aim of this book is to present some recent advances in the design of tunable detectors and the focus is on the so-called two-stage detectors, i.e., adaptive algorithms obtained cascading two detectors with opposite behaviors. We derive exact closed-form expressions for the resulting probability of false alarm and the probability of detection for both matched and mismatched signals embedded in homogeneous Gaussian noise. It turns out that such solutions guarantee a wide operational range in terms of tunability while retaining, at the same time, an overall performance in presence of matched signals commensurate with Kelly's detector. Table of Contents: Introduction / Adaptive Radar Detection of Targets / Adaptive Detection Schemes for Mismatched Signals / Enhanced Adaptive Sidelobe Blanking Algorithms / Conclusions
Book Synopsis Adaptive Radar Detection: Model-Based, Data-Driven and Hybrid Approaches by : Angelo Coluccia
Download or read book Adaptive Radar Detection: Model-Based, Data-Driven and Hybrid Approaches written by Angelo Coluccia and published by Artech House. This book was released on 2022-11-30 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows you how to adopt data-driven techniques for the problem of radar detection, both per se and in combination with model-based approaches. In particular, the focus is on space-time adaptive target detection against a background of interference consisting of clutter, possible jammers, and noise. It is a handy, concise reference for many classic (model-based) adaptive radar detection schemes as well as the most popular machine learning techniques (including deep neural networks) and helps you identify suitable data-driven approaches for radar detection and the main related issues. You’ll learn how data-driven tools relate to, and can be coupled or hybridized with, traditional adaptive detection statistics; understand fundamental concepts, schemes, and algorithms from statistical learning, classification, and neural networks domains. The book also walks you through how these concepts and schemes have been adapted for the problem of radar detection in the literature and provides you with a methodological guide for the design, illustrating different possible strategies. You’ll be equipped to develop a unified view, under which you can exploit the new possibilities of the data-driven approach even using simulated data. This book is an excellent resource for Radar professionals and industrial researchers, postgraduate students in electrical engineering and the academic community.
Book Synopsis Adaptive Detection of Multichannel Signals Exploiting Persymmetry by : Jun Liu
Download or read book Adaptive Detection of Multichannel Signals Exploiting Persymmetry written by Jun Liu and published by CRC Press. This book was released on 2022-12-20 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a systematic presentation of persymmetric adaptive detection, including detector derivations and the definition of key concepts, followed by detailed discussion relating to theoretical underpinnings, design methodology, design considerations, and techniques enabling its practical implementation. The received data for modern radar systems are usually multichannel, namely, vector-valued, or even matrix-valued. Multichannel signal detection in Gaussian backgrounds is a fundamental problem for radar applications. With an overarching focus on persymmetric adaptive detectors, this book presents the mathematical models and design principles necessary for analyzing the behavior of each kind of persymmetric adaptive detector. Building upon that, it also introduces new design approaches and techniques that will guide engineering students as well as radar engineers toward efficient detector solutions, especially in challenging sample-starved environments where training data are limited. This book will be of interest to students, scholars, and engineers in the field of signal processing. It will be especially useful for those who have a solid background in statistical signal processing, multivariate statistical analysis, matrix theory, and mathematical analysis.
Book Synopsis Advances in Adaptive Radar Detection and Range Estimation by : Chengpeng Hao
Download or read book Advances in Adaptive Radar Detection and Range Estimation written by Chengpeng Hao and published by Springer Nature. This book was released on 2021-12-03 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive and systematic framework for the design of adaptive architectures, which take advantage of the available a priori information to enhance the detection performance. Moreover, this framework also provides guidelines to develop decision schemes capable of estimating the target position within the range bin. To this end, the readers are driven step-by-step towards those aspects that have to be accounted for at the design stage, starting from the exploitation of system and/or environment information up to the use of target energy leakage (energy spillover), which allows inferring on the target position within the range cell under test.In addition to design issues, this book presents an extensive number of illustrative examples based upon both simulated and real-recorded data. Moreover, the performance analysis is enriched by considerations about the trade-off between performances and computational requirements.Finally, this book could be a valuable resource for PhD students, researchers, professors, and, more generally, engineers working on statistical signal processing and its applications to radar systems.
Download or read book Sonar Systems written by Nikolai Kolev and published by BoD – Books on Demand. This book was released on 2011-09-12 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an edited collection of research articles covering the current state of sonar systems, the signal processing methods and their applications prepared by experts in the field. The first section is dedicated to the theory and applications of innovative synthetic aperture, interferometric, multistatic sonars and modeling and simulation. Special section in the book is dedicated to sonar signal processing methods covering: passive sonar array beamforming, direction of arrival estimation, signal detection and classification using DEMON and LOFAR principles, adaptive matched field signal processing. The image processing techniques include: image denoising, detection and classification of artificial mine like objects and application of hidden Markov model and artificial neural networks for signal classification. The biology applications include the analysis of biosonar capabilities and underwater sound influence on human hearing. The marine science applications include fish species target strength modeling, identification and discrimination from bottom scattering and pelagic biomass neural network estimation methods. Marine geology has place in the book with geomorphological parameters estimation from side scan sonar images. The book will be interesting not only for specialists in the area but also for readers as a guide in sonar systems principles of operation, signal processing methods and marine applications.
Book Synopsis Smartphone-Based Real-Time Digital Signal Processing by : Nasser Kehtarnavaz
Download or read book Smartphone-Based Real-Time Digital Signal Processing written by Nasser Kehtarnavaz and published by Springer Nature. This book was released on 2015-08-19 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real-time or applied digital signal processing courses are offered as follow-ups to conventional or theory-oriented digital signal processing courses in many engineering programs for the purpose of teaching students the technical know-how for putting signal processing algorithms or theory into practical use. These courses normally involve access to a teaching laboratory that is equipped with hardware boards, in particular DSP boards, together with their supporting software. A number of textbooks have been written discussing how to achieve real-time implementation on these hardware boards. This book discusses how smartphones can be used as hardware boards for real-time implementation of signal processing algorithms as an alternative to the hardware boards that are currently being used in signal processing teaching laboratories. The fact that mobile devices, in particular smartphones, have now become powerful processing platforms has led to the development of this book, thus enabling students to use their own smartphones to run signal processing algorithms in real-time considering that these days nearly all students possess smartphones. Changing the hardware platforms that are currently used in applied or real-time signal processing courses to smartphones creates a truly mobile laboratory experience or environment for students. In addition, it relieves the cost burden associated with using a dedicated signal processing board noting that the software development tools for smartphones are free of charge and are well-developed. This book is written in such a way that it can be used as a textbook for applied or real time digital signal processing courses offered at many universities. Ten lab experiments that are commonly encountered in such courses are covered in the book. This book is written primarily for those who are already familiar with signal processing concepts and are interested in their real-time and practical aspects. Similar to existing real-time courses, knowledge of C programming is assumed. This book can also be used as a self-study guide for those who wish to become familiar with signal processing app development on either Android or iPhone smartphones. All the lab codes can be obtained as a software package from http://sites.fastspring.com/bookcodes/product/bookcodes
Book Synopsis Smartphone-Based Real-Time Digital Signal Processing, Second Edition by : Nasser Kehtarnavaz
Download or read book Smartphone-Based Real-Time Digital Signal Processing, Second Edition written by Nasser Kehtarnavaz and published by Springer Nature. This book was released on 2018-12-17 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real-time or applied digital signal processing courses are offered as follow-ups to conventional or theory-oriented digital signal processing courses in many engineering programs for the purpose of teaching students the technical know-how for putting signal processing algorithms or theory into practical use. These courses normally involve access to a teaching laboratory that is equipped with hardware boards, in particular DSP boards, together with their supporting software. A number of textbooks have been written discussing how to achieve real-time implementation on these hardware boards. This book discusses how to use smartphones as hardware boards for real-time implementation of signal processing algorithms as an alternative to the hardware boards that are used in signal processing laboratory courses. The fact that mobile devices, in particular smartphones, have become powerful processing platforms led to the development of this book enabling students to use their own smartphones to run signal processing algorithms in real-time considering that these days nearly all students possess smartphones. Changing the hardware platforms that are currently used in applied or real-time signal processing courses to smartphones creates a truly mobile laboratory experience or environment for students. In addition, it relieves the cost burden associated with using dedicated signal processing boards noting that the software development tools for smartphones are free of charge and are well-maintained by smartphone manufacturers. This book is written in such a way that it can be used as a textbook for real-time or applied digital signal processing courses offered at many universities. Ten lab experiments that are commonly encountered in such courses are covered in the book. This book is written primarily for those who are already familiar with signal processing concepts and are interested in their real-time and practical aspects. Similar to existing real-time courses, knowledge of C programming is assumed. This book can also be used as a self-study guide for those who wish to become familiar with signal processing app development on either Android or iPhone smartphones.
Book Synopsis Sequential Monte Carlo Methods for Nonlinear Discrete-Time Filtering by : Marcelo G.
Download or read book Sequential Monte Carlo Methods for Nonlinear Discrete-Time Filtering written by Marcelo G. and published by Springer Nature. This book was released on 2022-06-01 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt: In these notes, we introduce particle filtering as a recursive importance sampling method that approximates the minimum-mean-square-error (MMSE) estimate of a sequence of hidden state vectors in scenarios where the joint probability distribution of the states and the observations is non-Gaussian and, therefore, closed-form analytical expressions for the MMSE estimate are generally unavailable. We begin the notes with a review of Bayesian approaches to static (i.e., time-invariant) parameter estimation. In the sequel, we describe the solution to the problem of sequential state estimation in linear, Gaussian dynamic models, which corresponds to the well-known Kalman (or Kalman-Bucy) filter. Finally, we move to the general nonlinear, non-Gaussian stochastic filtering problem and present particle filtering as a sequential Monte Carlo approach to solve that problem in a statistically optimal way. We review several techniques to improve the performance of particle filters, including importance function optimization, particle resampling, Markov Chain Monte Carlo move steps, auxiliary particle filtering, and regularized particle filtering. We also discuss Rao-Blackwellized particle filtering as a technique that is particularly well-suited for many relevant applications such as fault detection and inertial navigation. Finally, we conclude the notes with a discussion on the emerging topic of distributed particle filtering using multiple processors located at remote nodes in a sensor network. Throughout the notes, we often assume a more general framework than in most introductory textbooks by allowing either the observation model or the hidden state dynamic model to include unknown parameters. In a fully Bayesian fashion, we treat those unknown parameters also as random variables. Using suitable dynamic conjugate priors, that approach can be applied then to perform joint state and parameter estimation. Table of Contents: Introduction / Bayesian Estimation of Static Vectors / The Stochastic Filtering Problem / Sequential Monte Carlo Methods / Sampling/Importance Resampling (SIR) Filter / Importance Function Selection / Markov Chain Monte Carlo Move Step / Rao-Blackwellized Particle Filters / Auxiliary Particle Filter / Regularized Particle Filters / Cooperative Filtering with Multiple Observers / Application Examples / Summary
Book Synopsis Processing of Seismic Reflection Data Using MATLAB by : Wail Mousa
Download or read book Processing of Seismic Reflection Data Using MATLAB written by Wail Mousa and published by Springer Nature. This book was released on 2022-05-31 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: This short book is for students, professors and professionals interested in signal processing of seismic data using MATLABTM. The step-by-step demo of the full reflection seismic data processing workflow using a complete real seismic data set places itself as a very useful feature of the book. This is especially true when students are performing their projects, and when professors and researchers are testing their new developed algorithms in MATLABTM for processing seismic data. The book provides the basic seismic and signal processing theory required for each chapter and shows how to process the data from raw field records to a final image of the subsurface all using MATLABTM. The MATLABTM codes and seismic data can be downloaded here. Table of Contents: Seismic Data Processing: A Quick Overview / Examination of A Real Seismic Data Set / Quality Control of Real Seismic Data / Seismic Noise Attenuation / Seismic Deconvolution / Carrying the Processing Forward / Static Corrections / Seismic Migration / Concluding Remarks
Book Synopsis An Introduction to Kalman Filtering with MATLAB Examples by : Narayan Kovvali
Download or read book An Introduction to Kalman Filtering with MATLAB Examples written by Narayan Kovvali and published by Springer Nature. This book was released on 2022-06-01 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Kalman filter is the Bayesian optimum solution to the problem of sequentially estimating the states of a dynamical system in which the state evolution and measurement processes are both linear and Gaussian. Given the ubiquity of such systems, the Kalman filter finds use in a variety of applications, e.g., target tracking, guidance and navigation, and communications systems. The purpose of this book is to present a brief introduction to Kalman filtering. The theoretical framework of the Kalman filter is first presented, followed by examples showing its use in practical applications. Extensions of the method to nonlinear problems and distributed applications are discussed. A software implementation of the algorithm in the MATLAB programming language is provided, as well as MATLAB code for several example applications discussed in the manuscript.
Book Synopsis Smartphone-Based Real-Time Digital Signal Processing, Third Edition by : Abhishek Sehgal
Download or read book Smartphone-Based Real-Time Digital Signal Processing, Third Edition written by Abhishek Sehgal and published by Springer Nature. This book was released on 2022-05-31 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real-time or applied digital signal processing courses are offered as follow-ups to conventional or theory-oriented digital signal processing courses in many engineering programs for the purpose of teaching students the technical know-how for putting signal processing algorithms or theory into practical use. These courses normally involve access to a teaching laboratory that is equipped with hardware boards, in particular DSP boards, together with their supporting software. A number of textbooks have been written discussing how to achieve real-time implementation on these hardware boards. This book discusses how to use smartphones as hardware boards for real-time implementation of signal processing algorithms, thus providing an alternative to the hardware boards that are used in signal processing laboratory courses. The fact that mobile devices, in particular smartphones, have become powerful processing platforms led to the development of this book to enable students to use their own smartphones to run signal processing algorithms in real-time considering that these days nearly all students possess smartphones. Changing the hardware platforms that are currently used in applied or real-time signal processing courses to smartphones creates a truly flexible laboratory experience or environment for students. In addition, it relieves the cost burden associated with using dedicated signal processing boards noting that the software development tools for smartphones are free of charge and are well-maintained by smartphone manufacturers. This book is written in such a way that it can be used as a textbook for real-time or applied digital signal processing courses offered at many universities. Ten lab experiments that are commonly encountered in such courses are covered in the book. It is written primarily for those who are already familiar with signal processing concepts and are interested in their real-time and practical aspects. Similar to existing real-time courses, knowledge of C programming is assumed. This book can also be used as a self-study guide for those who wish to become familiar with signal processing app development on either Android or iOS smartphones/tablets.
Book Synopsis Fixed-Point Signal Processing by : Wayne Padgett
Download or read book Fixed-Point Signal Processing written by Wayne Padgett and published by Springer Nature. This book was released on 2022-06-01 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to fill the gap between the ""ideal precision"" digital signal processing (DSP) that is widely taught, and the limited precision implementation skills that are commonly required in fixed-point processors and field programmable gate arrays (FPGAs). These skills are often neglected at the university level, particularly for undergraduates. We have attempted to create a resource both for a DSP elective course and for the practicing engineer with a need to understand fixed-point implementation. Although we assume a background in DSP, Chapter 2 contains a review of basic theory and Chapter 3 reviews random processes to support the noise model of quantization error. Chapter 4 details the binary arithmetic that underlies fixed-point processors and then introduces fractional format for binary numbers. Chapter 5 covers the noise model for quantization error and the effects of coefficient quantization in filters. Because of the numerical sensitivity of IIR filters, they are used extensively as an example system in both Chapters 5 and 6. Fortunately, the principles of dealing with limited precision can be applied to a wide variety of numerically sensitive systems, not just IIR filters. Chapter 6 discusses the problems of product roundoff error and various methods of scaling to avoid overflow. Chapter 7 discusses limit cycle effects and a few common methods for minimizing them. There are a number of simple exercises integrated into the text to allow you to test your understanding. Answers to the exercises are included in the footnotes. A number of MATLAB examples are provided in the text. They generally assume access to the Fixed-Point Toolbox. If you lack access to this software, consider either purchasing or requesting an evaluation license from The Mathworks. The code listed in the text and other helpful MATLAB code is also available at http://www.morganclaypool.com/page/padgett and http://www.rose-hulman.edu/padgett/fpsp. You will also find MATLAB exercises designed to demonstrate each of the four types of error discussed in Chapters 5 and 6. Simulink examples are also provided on the web site. Table of Contents: Getting Started / DSP Concepts / Random Processes and Noise / Fixed Point Numbers / Quantization Effects: Data and Coefficients / Quantization Effects - Round-Off Noise and Overflow / Limit Cycles
Book Synopsis Signals and Systems by : Khalid Sayood
Download or read book Signals and Systems written by Khalid Sayood and published by Springer Nature. This book was released on 2022-06-01 with total page 387 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed for use as a textbook for a one semester Signals and Systems class. It is sufficiently user friendly to be used for self study as well. It begins with a gentle introduction to the idea of abstraction by looking at numbers—the one highly abstract concept we use all the time. It then introduces some special functions that are useful for analyzing signals and systems. It then spends some time discussing some of the properties of systems; the goal being to introduce the idea of a linear time-invariant system which is the focus of the rest of the book. Fourier series, discrete and continuous time Fourier transforms are introduced as tools for the analysis of signals. The concepts of sampling and modulation which are very much a part of everyday life are discussed as applications of the these tools. Laplace transform and Z transform are then introduced as tools to analyze systems. The notions of stability of systems and feedback are analyzed using these tools. The book is divided into thirty bite-sized modules. Each module also links up with a video lecture through a QR code in each module. The video lectures are approximately thirty minutes long. There are a set of self study questions at the end of each module along with answers to help the reader reinforce the concepts in the module.
Book Synopsis Anywhere-Anytime Signals and Systems Laboratory by : Fatemeh Saki
Download or read book Anywhere-Anytime Signals and Systems Laboratory written by Fatemeh Saki and published by Springer Nature. This book was released on 2022-05-31 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: A typical undergraduate electrical engineering curriculum incorporates a signals and systems course. The widely used approach for the laboratory component of such courses involves the utilization of MATLAB to implement signals and systems concepts. This book presents a newly developed laboratory paradigm where MATLAB codes are made to run on smartphones which are possessed by nearly all students. As a result, this laboratory paradigm provides an anywhere-anytime hardware platform or processing board for students to learn implementation aspects of signals and systems concepts. The book covers the laboratory experiments that are normally covered in signals and systems courses and discusses how to run MATLAB codes for these experiments as apps on both Android and iOS smartphones, thus enabling a truly mobile laboratory paradigm. A zipped file of the codes discussed in the book can be acquired via the website http://sites.fastspring.com/bookcodes/product/SignalsSystemsBookcodesThirdEdition
Book Synopsis Anywhere-Anytime Signals and Systems Laboratory by : Nasser Kehtarnavaz
Download or read book Anywhere-Anytime Signals and Systems Laboratory written by Nasser Kehtarnavaz and published by Morgan & Claypool Publishers. This book was released on 2018-11-06 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: A typical undergraduate electrical engineering curriculum incorporates a signals and systems course. The widely used approach for the laboratory component of such courses involves the utilization of MATLAB to implement signals and systems concepts. This lecture series book presents a newly developed laboratory paradigm where MATLAB codes are made to run on smartphones, which most students already possess. This smartphone-based approach enables an anywhere-anytime platform for students to conduct signals and systems experiments. This book covers the laboratory experiments that are normally covered in signals and systems courses and discusses how to run MATLAB codes for these experiments on both Android and iOS smartphones, thus enabling a truly mobile laboratory environment for students to learn the implementation aspects of signals and systems concepts. A zipped file of the codes discussed in the book can be acquired via the website.
Book Synopsis Machine and Deep Learning Algorithms and Applications by : Uday Shankar
Download or read book Machine and Deep Learning Algorithms and Applications written by Uday Shankar and published by Springer Nature. This book was released on 2022-05-31 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces basic machine learning concepts and applications for a broad audience that includes students, faculty, and industry practitioners. We begin by describing how machine learning provides capabilities to computers and embedded systems to learn from data. A typical machine learning algorithm involves training, and generally the performance of a machine learning model improves with more training data. Deep learning is a sub-area of machine learning that involves extensive use of layers of artificial neural networks typically trained on massive amounts of data. Machine and deep learning methods are often used in contemporary data science tasks to address the growing data sets and detect, cluster, and classify data patterns. Although machine learning commercial interest has grown relatively recently, the roots of machine learning go back to decades ago. We note that nearly all organizations, including industry, government, defense, and health, are using machine learning to address a variety of needs and applications. The machine learning paradigms presented can be broadly divided into the following three categories: supervised learning, unsupervised learning, and semi-supervised learning. Supervised learning algorithms focus on learning a mapping function, and they are trained with supervision on labeled data. Supervised learning is further sub-divided into classification and regression algorithms. Unsupervised learning typically does not have access to ground truth, and often the goal is to learn or uncover the hidden pattern in the data. Through semi-supervised learning, one can effectively utilize a large volume of unlabeled data and a limited amount of labeled data to improve machine learning model performances. Deep learning and neural networks are also covered in this book. Deep neural networks have attracted a lot of interest during the last ten years due to the availability of graphics processing units (GPU) computational power, big data, and new software platforms. They have strong capabilities in terms of learning complex mapping functions for different types of data. We organize the book as follows. The book starts by introducing concepts in supervised, unsupervised, and semi-supervised learning. Several algorithms and their inner workings are presented within these three categories. We then continue with a brief introduction to artificial neural network algorithms and their properties. In addition, we cover an array of applications and provide extensive bibliography. The book ends with a summary of the key machine learning concepts.
Book Synopsis Linear Algebra for Pattern Processing by : Kenichi Kanatani
Download or read book Linear Algebra for Pattern Processing written by Kenichi Kanatani and published by Springer Nature. This book was released on 2022-06-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra is one of the most basic foundations of a wide range of scientific domains, and most textbooks of linear algebra are written by mathematicians. However, this book is specifically intended to students and researchers of pattern information processing, analyzing signals such as images and exploring computer vision and computer graphics applications. The author himself is a researcher of this domain. Such pattern information processing deals with a large amount of data, which are represented by high-dimensional vectors and matrices. There, the role of linear algebra is not merely numerical computation of large-scale vectors and matrices. In fact, data processing is usually accompanied with "geometric interpretation." For example, we can think of one data set being "orthogonal" to another and define a "distance" between them or invoke geometric relationships such as "projecting" some data onto some space. Such geometric concepts not only help us mentally visualize abstract high-dimensional spaces in intuitive terms but also lead us to find what kind of processing is appropriate for what kind of goals. First, we take up the concept of "projection" of linear spaces and describe "spectral decomposition," "singular value decomposition," and "pseudoinverse" in terms of projection. As their applications, we discuss least-squares solutions of simultaneous linear equations and covariance matrices of probability distributions of vector random variables that are not necessarily positive definite. We also discuss fitting subspaces to point data and factorizing matrices in high dimensions in relation to motion image analysis. Finally, we introduce a computer vision application of reconstructing the 3D location of a point from three camera views to illustrate the role of linear algebra in dealing with data with noise. This book is expected to help students and researchers of pattern information processing deepen the geometric understanding of linear algebra.
