Multidimensional Discrete Unitary Transforms

Multidimensional Discrete Unitary Transforms

Illustrating methods to construct new unitary transforms for best algorithm selection and development in real-world applications, the book contains a wide range of examples to compare the efficacy of different algorithms in a variety of one ...

Author: Artyom M. Grigoryan

Publisher: CRC Press

ISBN: 0824745965

Category: Technology & Engineering

Page: 544

View: 658

This reference presents a more efficient, flexible, and manageable approach to unitary transform calculation and examines novel concepts in the design, classification, and management of fast algorithms for different transforms in one-, two-, and multidimensional cases. Illustrating methods to construct new unitary transforms for best algorithm selection and development in real-world applications, the book contains a wide range of examples to compare the efficacy of different algorithms in a variety of one-, two-, and three-dimensional cases. Multidimensional Discrete Unitary Transforms builds progressively from simple representative cases to higher levels of generalization.
Categories: Technology & Engineering

Transforms and Applications Handbook

Transforms and Applications Handbook

Multidimensional. Discrete. Unitary. Transforms. 19-1 19-5 19-7 19-10 19-16 19.1 Introduction. ... Radix Algorithm • Method of the Polynomial Transforms 19.2 Nontraditional Forms of 19.3 Partitioning of Multidimensional Transforms .

Author: Alexander D. Poularikas

Publisher: CRC Press

ISBN: 9781420066531

Category: Mathematics

Page: 911

View: 834

Updating the original, Transforms and Applications Handbook, Third Edition solidifies its place as the complete resource on those mathematical transforms most frequently used by engineers, scientists, and mathematicians. Highlighting the use of transforms and their properties, this latest edition of the bestseller begins with a solid introduction to signals and systems, including properties of the delta function and some classical orthogonal functions. It then goes on to detail different transforms, including lapped, Mellin, wavelet, and Hartley varieties. Written by top experts, each chapter provides numerous examples and applications that clearly demonstrate the unique purpose and properties of each type. The material is presented in a way that makes it easy for readers from different backgrounds to familiarize themselves with the wide range of transform applications. Revisiting transforms previously covered, this book adds information on other important ones, including: Finite Hankel, Legendre, Jacobi, Gengenbauer, Laguerre, and Hermite Fraction Fourier Zak Continuous and discrete Chirp-Fourier Multidimensional discrete unitary Hilbert-Huang Most comparable books cover only a few of the transforms addressed here, making this text by far the most useful for anyone involved in signal processing—including electrical and communication engineers, mathematicians, and any other scientist working in this field.
Categories: Mathematics

Image Processing

Image Processing

Tensor Transform and Discrete Tomography with MATLAB ® Artyom M. Grigoryan, Merughan M. Grigoryan ... A.M. Grigoryan and S.S. Agaian, Multidimensional Discrete Unitary Transforms: Representation, Partitioning and Algorithms,” Marcel ...

Author: Artyom M. Grigoryan

Publisher: CRC Press

ISBN: 9781351832373

Category: Technology & Engineering

Page: 466

View: 431

Focusing on mathematical methods in computer tomography, Image Processing: Tensor Transform and Discrete Tomography with MATLAB® introduces novel approaches to help in solving the problem of image reconstruction on the Cartesian lattice. Specifically, it discusses methods of image processing along parallel rays to more quickly and accurately reconstruct images from a finite number of projections, thereby avoiding overradiation of the body during a computed tomography (CT) scan. The book presents several new ideas, concepts, and methods, many of which have not been published elsewhere. New concepts include methods of transferring the geometry of rays from the plane to the Cartesian lattice, the point map of projections, the particle and its field function, and the statistical model of averaging. The authors supply numerous examples, MATLAB®-based programs, end-of-chapter problems, and experimental results of implementation. The main approach for image reconstruction proposed by the authors differs from existing methods of back-projection, iterative reconstruction, and Fourier and Radon filtering. In this book, the authors explain how to process each projection by a system of linear equations, or linear convolutions, to calculate the corresponding part of the 2-D tensor or paired transform of the discrete image. They then describe how to calculate the inverse transform to obtain the reconstruction. The proposed models for image reconstruction from projections are simple and result in more accurate reconstructions. Introducing a new theory and methods of image reconstruction, this book provides a solid grounding for those interested in further research and in obtaining new results. It encourages readers to develop effective applications of these methods in CT.
Categories: Technology & Engineering

Computer Aided Systems Theory EUROCAST 2009

Computer Aided Systems Theory   EUROCAST 2009

Agaian, S., Astola, J., Egiazarian, K.: Binary Polynomial Transforms and Nonlinear Digital Filters. ... (2008) Grigoryan, A., Agaian, S.: Multidimensional Discrete Unitary Transformations: Representation, Partitioning, and Algorithms.

Author: Roberto Moreno Díaz

Publisher: Springer

ISBN: 9783642047725

Category: Computers

Page: 950

View: 252

The concept of CAST as Computer Aided Systems Theory was introduced by F. Pichler in the late 1980s to refer to computer theoretical and practical developments as tools for solving problems in system science. It was thought of as the third component (the other two being CAD and CAM) required to complete the path from computer and systems sciences to practical developments in science and engineering. Franz Pichler, of the University of Linz, organized the first CAST workshop in April 1988, which demonstrated the acceptance of the concepts by the scientific and technical community. Next, the University of Las Palmas de Gran Canaria joined the University of Linz to organize the first international meeting on CAST (Las Palmas, February 1989) under the name EUROCAST'89. This proved to be a very successful gathering of systems theorists, computer scientists and engineers from most European countries, North America and Japan. It was agreed that EUROCAST international conferences would be organized every two years, alternating between Las Palmas de Gran Canaria and a continental European location. From 2001 the conference has been held exclusively in Las Palmas. Thus, successive EUROCAST meetings took place in Krems (1991), Las Palmas (1993), In- bruck (1995), Las Palmas (1997), Vienna (1999), Las Palmas (2001), Las Palmas (2003) Las Palmas (2005) and Las Palmas (2007), in addition to an extra-European CAST c- ference in Ottawa in 1994.
Categories: Computers

Medical Image Processing Reconstruction and Analysis

Medical Image Processing  Reconstruction and Analysis

2.3 DISCRETE TWO-DIMENSIONAL LINEAR TRANSFORMS Any concrete image (sc., original image) can be considered a linear ... (f i,k ) (Fm,n ) (Gm,n ) (g i,k ) 2D unitary transform spectral domain processing 2D inverse transform FIGURE 2.15 ...

Author: Jiri Jan

Publisher: CRC Press

ISBN: 9781351387910

Category: Medical

Page: 574

View: 688

Differently oriented specialists and students involved in image processing and analysis need to have a firm grasp of concepts and methods used in this now widely utilized area. This book aims at being a single-source reference providing such foundations in the form of theoretical yet clear and easy to follow explanations of underlying generic concepts. Medical Image Processing, Reconstruction and Analysis – Concepts and Methods explains the general principles and methods of image processing and analysis, focusing namely on applications used in medical imaging. The content of this book is divided into three parts: Part I – Images as Multidimensional Signals provides the introduction to basic image processing theory, explaining it for both analogue and digital image representations. Part II – Imaging Systems as Data Sources offers a non-traditional view on imaging modalities, explaining their principles influencing properties of the obtained images that are to be subsequently processed by methods described in this book. Newly, principles of novel modalities, as spectral CT, functional MRI, ultrafast planar-wave ultrasonography and optical coherence tomography are included. Part III – Image Processing and Analysis focuses on tomographic image reconstruction, image fusion and methods of image enhancement and restoration; further it explains concepts of low-level image analysis as texture analysis, image segmentation and morphological transforms. A new chapter deals with selected areas of higher-level analysis, as principal and independent component analysis and particularly the novel analytic approach based on deep learning. Briefly, also the medical image-processing environment is treated, including processes for image archiving and communication. Features Presents a theoretically exact yet understandable explanation of image processing and analysis concepts and methods Offers practical interpretations of all theoretical conclusions, as derived in the consistent explanation Provides a concise treatment of a wide variety of medical imaging modalities including novel ones, with respect to properties of provided image data
Categories: Medical

Multidimensional Analysis and Discrete Models

Multidimensional Analysis and Discrete Models

Then Atu(t)=U-1(t)U(t+1)efi, where 5 is a group of unitary transformations of H, and a natural analog of the dynamic postulate (8) should be a law of the form Atu(t,f)=(p(f(t))), where b : H → 5 is a given map. However, in actual fact, ...

Author: Aleksei A. Dezin

Publisher: CRC Press

ISBN: 9781351091763

Category: Mathematics

Page: 252

View: 386

Multidimensional Analysis and Discrete Models, a thorough and detailed reference, covers the main structures of multidimensional analysis and the intrinsically defined discrete models in applied mathematics, mathematical physics, and related fields. The material is presented in a clear and straightforward manner, with background information provided to define finite models and to clarify the concepts of multidimensional analysis. The book covers special difference models of the mathematical physics equations, models of boundary value problems, and objects of quantum mechanics. Considerable attention is also given to differential operators on Riemannian manifolds and the interpretation of classical vector analysis. The primary focus of Multidimensional Analysis and Discrete Models is on the description of regular methods of constructing intrinsically defined discrete models for special classes of continual objects, but emphasis is also given to the interaction of ideas and methods that exist throughout the field of mathematics. For example, the connections between theories derived from classical and functional analysis, Riemannian geometry, and algebraic topology are illustrated, and are discussed in terms of their relevance to computing solutions.
Categories: Mathematics

Digital Video Image Quality and Perceptual Coding

Digital Video Image Quality and Perceptual Coding

Multidimensional Discrete Unitary Transforms: Representation: Partitioning and Algorithms, Artyom M. Grigoryan, Sos S. Agaian, S.S. Agaian 19. High-Resolution and Robust Signal Processing, Yingbo Hua, Alex B. Gershman and Qi Cheng 20.

Author: H.R. Wu

Publisher: CRC Press

ISBN: 1420027824

Category: Technology & Engineering

Page: 640

View: 980

The hand is quicker than the eye. In many cases, so is digital video. Maintaining image quality in bandwidth- and memory-restricted environments is quickly becoming a reality as thriving research delves ever deeper into perceptual coding techniques, which discard superfluous data that humans cannot process or detect. Surveying the topic from a Human Visual System (HVS)-based approach, Digital Video Image Quality and Perceptual Coding outlines the principles, metrics, and standards associated with perceptual coding, as well as the latest techniques and applications. This book is divided broadly into three parts. First, it introduces the fundamental theory, concepts, principles, and techniques underlying the field, such as the basics of compression, HVS modeling, and coding artifacts associated with current well-known techniques. The next section focuses on picture quality assessment criteria; subjective and objective methods and metrics, including vision model based digital video impairment metrics; testing procedures; and international standards regarding image quality. Finally, practical applications come into focus, including digital image and video coder designs based on the HVS as well as post-filtering, restoration, error correction, and concealment techniques. The permeation of digital images and video throughout the world cannot be understated. Nor can the importance of preserving quality while using minimal storage space, and Digital Video Image Quality and Perceptual Coding provides the tools necessary to accomplish this goal. Instructors and lecturers wishing to make use of this work as a textbook can download a presentation of 786 slides in PDF format organized to augment the text. accompany our book (H.R. Wu and K.R. Rao, Digital Video Image Quality and Perceptual Coding, CRC Press (ISBN: 0-8247-2777-0), Nov. 2005) for lecturers or instructor to use for their classes if they use the book.
Categories: Technology & Engineering

Domain Specific Processors

Domain Specific Processors

Multidimensional Discrete Unitary Transforms : Representation , Partitioning , and Algorithms , Artyom M. Grigoryan and Sos A. Agaian 19. High - Resolution and Robust Signal Processing , Yingbo Hua , Alex B. Gershman , and Qi Cheng 20.

Author: Shuvra S. Bhattacharyya

Publisher: CRC Press

ISBN: 0203913183

Category: Computers

Page: 280

View: 973

Ranging from low-level application and architecture optimizations to high-level modeling and exploration concerns, this authoritative reference compiles essential research on various levels of abstraction appearing in embedded systems and software design. It promotes platform-based design for improved system implementation and modeling and enhanced
Categories: Computers

Image Processing Technologies

Image Processing Technologies

Multidimensional Discrete Unitary Transforms: Representation, Partitioning, and Algorithms, Artyom M. Grigoryan and Sos A. Agaian 19. High-Resolution and Robust Signal Processing, Yingbo Hua, Alex B. Gershman, and Qi Cheng 20.

Author: Kiyoharu Aizawa

Publisher: CRC Press

ISBN: 9780824754860

Category: Computers

Page: 296

View: 401

Showcasing the most influential developments, experiments, and architectures impacting the digital, surveillance, automotive, industrial, and medical sciences, this text/reference tracks the evolution and advancement of CVIP technologies - examining methods and algorithms for image analysis, optimization, segmentation, and restoration.
Categories: Computers

Digital Image Processing with Application to Digital Cinema

Digital Image Processing with Application to Digital Cinema

x 6 Discrete Transforms for Image Processing 123 6.1 Introduction 123 6.2 Unitary Transforms 123 6.2.1 One-Dimensional Unitary Transforms 123 6.2.1.1 One-Dimensional DFT 124 6.2.1.2 One-Dimensional Discrete Cosine Transform (DCT) 125 ...

Author: K. S. Thyagarajan

Publisher: Taylor & Francis

ISBN: 9780240807294

Category: Computers

Page: 378

View: 493

With crystal clarity, this book conveys the most current principles in digital image processing, providing both the background theory and the practical applications to various industries, such as digital cinema, video compression, and streaming media. This book contains tons of useful features, including: * a chapter on the role of human vision in image visualization, * the MATLAB codes used to generate most of the figures and tables listed in the book, as well as a few MATLAB projects, * a 24-pg color insert * case studies to illustrate the practical application of the theory.
Categories: Computers

Digital Image Processing

Digital Image Processing

3.4.4 Multidimensional FFT Algorithms Generally, there are two possibilities to develop fast algorithms for multidimensional discrete Fourier transforms. ... 2 3 3.4 Fast Algorithms for Unitary Transforms 75 Multidimensional FFT Algorithms.

Author: Bernd Jähne

Publisher: Springer Science & Business Media

ISBN: 9783662115657

Category: Technology & Engineering

Page: 383

View: 325

Intended as a practical guide, the book takes the reader from basic concepts to up-to-date research topics in digital image processing. Only little special knowledge in computer sciences is required since many principles and mathematical tools widely used in natural sciences are also applied in digital image processing thus the reader with a general background in natural science gets an easy access to the material presented. The book discusses the following topics: image acquisition and digitization; linear and nonlinear filter operations; edge detection; local orientation and texture; fast algorithms on pyramidal and multigrid data structures; morphological operations to detect the shape of objects; segmentation and classification. Further chapters deal with the reconstruction of three-dimensional objects from projections and the analysis of stereo images and image sequences with differential, correlation, and filter algorithms. Many examples from different areas show how the reader can use digital image processing as an experimental tool for image data acquisition and evaluation in his or her research area.
Categories: Technology & Engineering

Applications of Digital Image Processing

Applications of Digital Image Processing

Superfast Algorithms of Multidimensional Discrete k - Wave Transforms and Volterra Filtering Based on Superfast ... for a wide class of non - separable n - dimensional ( nD ) discrete unitary K - transforms ( DKT ) are introduced .

Author:

Publisher:

ISBN: UOM:39015047826261

Category: Image processing

Page:

View: 814

Categories: Image processing

Multidimensional Quantum Dynamics

Multidimensional Quantum Dynamics

10.4 Symmetry-Adapted Correlation Discrete Variable Representation Symmetry-related issues can become particularly ... whenever the position operator matrix representation has degenerate eigenvalues, a unitary transformation cannot be ...

Author: Hans-Dieter Meyer

Publisher: John Wiley & Sons

ISBN: 9783527627417

Category: Science

Page: 442

View: 216

The first book dedicated to this new and powerful computational method begins with a comprehensive description of MCTDH and its theoretical background. There then follows a discussion of recent extensions of MCTDH, such as the treatment of identical particles, leading to the MCTDHF and MCTDHB methods for fermions and bosons. The third section presents a wide spectrum of very different applications to reflect the large diversity of problems that can be tackled by MCTDH. The result is handbook and ready reference for theoretical chemists, physicists, chemists, graduate students, lecturers and software producers.
Categories: Science

Medical Image Processing Reconstruction and Restoration

Medical Image Processing  Reconstruction and Restoration

65 2.2 Discrete Two-Dimensional Operators.................................... 67 2.2.1 Discrete Linear Two-Dimensional Operators........... 69 2.2.1.1 Generic Operators. ... 89 2.3.1 Two-Dimensional Unitary Transforms Generally.

Author: Jiri Jan

Publisher: CRC Press

ISBN: 9781420030679

Category: Medical

Page: 760

View: 223

It is essential that differently oriented specialists and students involved in image processing have a firm grasp of the necessary concepts and principles. A single-source reference that can provide this foundation, as well as a thorough explanation of the techniques involved, particularly those found in medical image processing, would be an
Categories: Medical

Numerical Grid Methods and Their Application to Schr dinger s Equation

Numerical Grid Methods and Their Application to Schr  dinger   s Equation

Similarly, the two-dimensional transformation matrix from the spectral to the DVR basis, f anmfahf L}moa = T.'ong, ... the transformation matrix L connects a grid space and a spectral space of different dimensions, it cannot be unitary.

Author: C. Cerjan

Publisher: Springer Science & Business Media

ISBN: 9789401582407

Category: Science

Page: 248

View: 425

The use of numerical grid methods to solve the Schrodinger equation has rapidly evolved in the past decade.The early attempts to demonstrate the computational viability of grid methods have been largely superseded by applications to specific problems and deeper research into more sophisticated quadrature schemes. Underpinning this research, of course, is the belief that the generic nature of grid methods can enjoy a symbiotic development with advances in computer technology, harnessing this technology in an effective manner. The contributions to this proceedings demonstrate these points in full: several appli cations displayed creative use and extension of existing grid methodology; other research concentrated on the development of new quadrature schemes or mixed numerical meth ods. The research represented ranges from highly specific spectral simulations of van der Waals complexs to general schemes for reactive scattering. The novelty of grid methods in Density Functional Theory calculations should also be highlighted since it represents an alternative to standard basis set expansion techniques and might offer distinct advantages to the standard techniques. A deliberate attempt was made to present research material with more motivational and background discussion than is typical of research publications. It is hoped that these contributed proceedings will be useful to students and researchers outside the field to have a rapid and complete introduction to many of the exciting uses of grid methodology in atomic and molecular physics. Special thanks are due to the NATO Science Committee for its generous support of the activities of this workshop.
Categories: Science

Selected Papers in Multidimensional Digital Signal Processing

Selected Papers in Multidimensional Digital Signal Processing

Multidimensional Signal Processing Committee. TABLE III TYPICAL FAST UNITARY TRANSFORM USED IN IMAGE PROCESSING Transform Formula Discrete Fourier ( DFT ) ; 21 ( MN 1 THU ° m , n Discrete Cosine ( DCT ) 1 Ni m = 1 , Isn & N . amin w cos ...

Author: IEEE Acoustics, Speech, and Signal Processing Society. Multidimensional Signal Processing Committee

Publisher: IEEE

ISBN: STANFORD:36105032986668

Category: Technology & Engineering

Page: 484

View: 236

Categories: Technology & Engineering

Digital Signal Filtering Analysis and Restoration

Digital Signal Filtering  Analysis and Restoration

The property of separability in this strict sense is also typical for unitary transforms , including the two - dimensional discrete Fourier transform . Another special case of an operator in eqn ( 14.19 ) is isoplanar operators for ...

Author: Jiří Jan

Publisher: IET

ISBN: 0852967608

Category: Technology & Engineering

Page: 407

View: 751

In the belief that every engineer and scientist working with signals or data should have a knowledge of them, Jan (electrical engineering and computer science, Technical U. of Brno, Czech Republic) explains some of the theoretical concepts that underlie the methods now in common use to process and analyze signals and data. He examines such topics as classical digital filtering, averaging methods to improve the signal-to-noise ratio of repetitive signals, correlation and spectral analysis, methods to estimate and define unknown signals, non-linear processing and neural networks, and multidimensional signals and data. The Czech original Cislicova filtrace, analyza a resaurace signalu was published by Vutium Press, Brno, in 1997. c. Book News Inc.
Categories: Technology & Engineering

Handbook of Image Processing and Computer Vision

Handbook of Image Processing and Computer Vision

2.3 Two-Dimensional Discrete Linear Transformation In the two-dimensional case, let's consider the discrete image f ... T is a unitary matrix analogous to that seen for the one-dimensional transform and F unit symmetric transformation.

Author: Arcangelo Distante

Publisher: Springer Nature

ISBN: 9783030423742

Category: Computers

Page: 432

View: 966

Across three volumes, the Handbook of Image Processing and Computer Vision presents a comprehensive review of the full range of topics that comprise the field of computer vision, from the acquisition of signals and formation of images, to learning techniques for scene understanding. The authoritative insights presented within cover all aspects of the sensory subsystem required by an intelligent system to perceive the environment and act autonomously. Volume 2 (From Image to Pattern) examines image transforms, image restoration, and image segmentation. Topics and features: • Describes the fundamental processes in the field of artificial vision that enable the formation of digital images from light energy • Covers light propagation, color perception, optical systems, and the analog-to-digital conversion of the signal • Discusses the information recorded in a digital image, and the image processing algorithms that can improve the visual qualities of the image • Reviews boundary extraction algorithms, key linear and geometric transformations, and techniques for image restoration • Presents a selection of different image segmentation algorithms, and of widely-used algorithms for the automatic detection of points of interest • Examines important algorithms for object recognition, texture analysis, 3D reconstruction, motion analysis, and camera calibration • Provides an introduction to four significant types of neural network, namely RBF, SOM, Hopfield, and deep neural networks This all-encompassing survey offers a complete reference for all students, researchers, and practitioners involved in developing intelligent machine vision systems. The work is also an invaluable resource for professionals within the IT/software and electronics industries involved in machine vision, imaging, and artificial intelligence. Dr. Cosimo Distante is a Research Scientist in Computer Vision and Pattern Recognition in the Institute of Applied Sciences and Intelligent Systems (ISAI) at the Italian National Research Council (CNR). Dr. Arcangelo Distante is a researcher and the former Director of the Institute of Intelligent Systems for Automation (ISSIA) at the CNR. His research interests are in the fields of Computer Vision, Pattern Recognition, Machine Learning, and Neural Computation.
Categories: Computers

Advances in Image and Graphics Technologies

Advances in Image and Graphics Technologies

3.1 The Prove of Fourier Transform Translation Theory of Three Dimensional Vector Matrix If f(x, y, z) → F(u, v, t), ... eight-order vector matrix for the unitary transformation matrix of - - #T . - - - Discrete Fourier Transform.

Author: Tieniu Tan

Publisher: Springer

ISBN: 9783662477915

Category: Computers

Page: 456

View: 564

This book constitutes the refereed proceedings of the 10th Chinese Conference on Advances in Image and Graphics Technologies, IGTA 2015, held in Beijing, China, in June 2015. The 50 papers presented were carefully reviewed and selected from 138 submissions. They provide a forum for sharing new aspects of the progresses in the areas of image processing technology, image analysis und understanding, computer vision and pattern recognition, big data mining, computer graphics and VR, image technology application.
Categories: Computers

Visual Information Processing

Visual Information Processing

discrete case . We have described methods of ... S. Deans , The Radon Transform and some of its Applications , Malabar , FL : Krieger , 1983 . 7. ... A.M. Grigoryan , Multidimensional Discrete Unitary Transforms : Representation ...

Author:

Publisher:

ISBN: UOM:39015058771760

Category: Image processing

Page:

View: 778

Categories: Image processing