Mathematical Methods For Signal And Image Analysis And Representation

Mathematical Methods for Signal and Image Analysis and Representation presents the mathematical methodology for generic image analysis tasks. In the context of this book an image may be any m-dimensional empirical signal living on an n-dimensional smooth manifold (typically, but not necessarily, a subset of spacetime). The existing literature on image methodology is rather scattered and often limited to either a deterministic or a statistical point of view. In contrast, this book brings together these seemingly different points of view in order to stress their conceptual relations and formal analogies. Furthermore, it does not focus on specific applications, although some are detailed for the sake of illustration, but on the methodological frameworks on which such applications are built, making it an ideal companion for those seeking a rigorous methodological basis for specific algorithms as well as for those interested in the fundamental methodology per se. Covering many topics at the forefront of current research, including anisotropic diffusion filtering of tensor fields, this book will be of particular interest to graduate and postgraduate students and researchers in the fields of computer vision, medical imaging and visual perception.

Mathematical Methods for Signal and Image Analysis and Representation presents the mathematical methodology for generic image analysis tasks. In the context of this book an image may be any m-dimensional empirical signal living on an n-dimensional smooth manifold (typically, but not necessarily, a subset of spacetime). The existing literature on image methodology is rather scattered and often limited to either a deterministic or a statistical point of view. In contrast, this book brings together these seemingly different points of view in order to stress their conceptual relations and formal analogies. Furthermore, it does not focus on specific applications, although some are detailed for the sake of illustration, but on the methodological frameworks on which such applications are built, making it an ideal companion for those seeking a rigorous methodological basis for specific algorithms as well as for those interested in the fundamental methodology per se. Covering many topics at the forefront of current research, including anisotropic diffusion filtering of tensor fields, this book will be of particular interest to graduate and postgraduate students and researchers in the fields of computer vision, medical imaging and visual perception.

Signal Processing: A Mathematical Approach is designed to show how many of the mathematical tools the reader knows can be used to understand and employ signal processing techniques in an applied environment. Assuming an advanced undergraduate- or graduate-level understanding of mathematics—including familiarity with Fourier series, matrices, probability, and statistics—this Second Edition: Contains new chapters on convolution and the vector DFT, plane-wave propagation, and the BLUE and Kalman filters Expands the material on Fourier analysis to three new chapters to provide additional background information Presents real-world examples of applications that demonstrate how mathematics is used in remote sensing Featuring problems for use in the classroom or practice, Signal Processing: A Mathematical Approach, Second Edition covers topics such as Fourier series and transforms in one and several variables; applications to acoustic and electro-magnetic propagation models, transmission and emission tomography, and image reconstruction; sampling and the limited data problem; matrix methods, singular value decomposition, and data compression; optimization techniques in signal and image reconstruction from projections; autocorrelations and power spectra; high-resolution methods; detection and optimal filtering; and eigenvector-based methods for array processing and statistical filtering, time-frequency analysis, and wavelets.

This previously included a CD. The CD contents can be accessed via World Wide Web.

International specialists report recent research and development, focusing on new applications: The book records proceedings of the IMA (Institution of Mathematics and Applications) conference co-sponsored with the Institute of Physics and the Institution of Electrical Engineers. Contents: Noise analysis: binary random images superposition: probabilistic image smoothing; Segmentation and pattern recognition; image segmentation; colour pattern recognition: Finger print identification; algorithms of 3-D Iso surfaces; mathematical model of image segmentation 3-D on parametric segmentation method: Artificial intelligence; Automatic satellite target detection; Analysis in light, confocal and electron microscopes; Compression Issues; Artificial neural networks; Coefficient video modelling; Progressive transmission: smoothing facsimile images; Human face identification; Fractals and wavelets; lacunarity; Wavelet processing of coloured images; Optical flow analysis; Computing optical fl

A thorough guide to the classical and contemporary mathematical methods of modern signal and image processing Discrete Fourier Analysis and Wavelets presents a thorough introduction to the mathematical foundations of signal and image processing. Key concepts and applications are addressed in a thought-provoking manner and are implemented using vector, matrix, and linear algebra methods. With a balanced focus on mathematical theory and computational techniques, this self-contained book equips readers with the essential knowledge needed to transition smoothly from mathematical models to practical digital data applications. The book first establishes a complete vector space and matrix framework for analyzing signals and images. Classical methods such as the discrete Fourier transform, the discrete cosine transform, and their application to JPEG compression are outlined followed by coverage of the Fourier series and the general theory of inner product spaces and orthogonal bases. The book then addresses convolution, filtering, and windowing techniques for signals and images. Finally, modern approaches are introduced, including wavelets and the theory of filter banks as a means of understanding the multiscale localized analysis underlying the JPEG 2000 compression standard. Throughout the book, examples using image compression demonstrate how mathematical theory translates into application. Additional applications such as progressive transmission of images, image denoising, spectrographic analysis, and edge detection are discussed. Each chapter provides a series of exercises as well as a MATLAB project that allows readers to apply mathematical concepts to solving real problems. Additional MATLAB routines are available via the book's related Web site. With its insightful treatment of the underlying mathematics in image compression and signal processing, Discrete Fourier Analysis and Wavelets is an ideal book for mathematics, engineering, and computer science courses at the upper-undergraduate and beginning graduate levels. It is also a valuable resource for mathematicians, engineers, and other practitioners who would like to learn more about the relevance of mathematics in digital data processing.

Digital image processing technology has developed markedly over the last ten years, and more and more information is being conveyed through its display and analysis. The way in which image data is stored and processed is fundamental to all aspects of information technology. Examples include remote sensing using digital satellites; making diagnoses using conventional X-ray computed tomography; and research into the behavior of the human brain using magnetic resonance imaging. This book consists of twenty-one papers that collectively cover a broad range of image processing problems and the way in which their solutions are used in different areas of science and technology. The papers present details of the ways computers of varying processing power can be programmed to store images efficiently, resolve features and patterns that are either time consuming or impossible for humans to interpret, and develop machines that can "see" like humans. They also discuss a wide range of applications, including the use of lasers for studying dynamic behavior of mechanical components, and fractal geometry for recognizing patterns. The book will be useful to any engineer, scientist, and technologist interested in current research issues in image processing.

Continuing in the footsteps of the pioneering first edition, Signal and Image Processing for Remote Sensing, Second Edition explores the most up-to-date signal and image processing methods for dealing with remote sensing problems. Although most data from satellites are in image form, signal processing can contribute significantly in extracting information from remotely sensed waveforms or time series data. This book combines both, providing a unique balance between the role of signal processing and image processing. Featuring contributions from worldwide experts, this book continues to emphasize mathematical approaches. Not limited to satellite data, it also considers signals and images from hydroacoustic, seismic, microwave, and other sensors. Chapters cover important topics in signal and image processing and discuss techniques for dealing with remote sensing problems. Each chapter offers an introduction to the topic before delving into research results, making the book accessible to a broad audience. This second edition reflects the considerable advances that have occurred in the field, with 23 of 27 chapters being new or entirely rewritten. Coverage includes new mathematical developments such as compressive sensing, empirical mode decomposition, and sparse representation, as well as new component analysis methods such as non-negative matrix and tensor factorization. The book also presents new experimental results on SAR and hyperspectral image processing. The emphasis is on mathematical techniques that will far outlast the rapidly changing sensor, software, and hardware technologies. Written for industrial and academic researchers and graduate students alike, this book helps readers connect the "dots" in image and signal processing. New in This Edition The second edition includes four chapters from the first edition, plus 23 new or entirely rewritten chapters, and 190 new figures. New topics covered include: Compressive sensing The mixed pixel problem with hyperspectral images Hyperspectral image (HSI) target detection and classification based on sparse representation An ISAR technique for refocusing moving targets in SAR images Empirical mode decomposition for signal processing Feature extraction for classification of remote sensing signals and images Active learning methods in classification of remote sensing images Signal subspace identification of hyperspectral data Wavelet-based multi/hyperspectral image restoration and fusion The second edition is not intended to replace the first edition entirely and readers are encouraged to read both editions of the book for a more complete picture of signal and image processing in remote sensing. See Signal and Image Processing for Remote Sensing (CRC Press 2006).