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Inversion-Based Fourier Transform as a New Tool for Noise Rejection

Inversion-Based Fourier Transform as a New Tool for Noise Rejection
Author: Mihály Dobróka
Publisher:
Total Pages:
Release: 2017
Genre: Mathematics
ISBN:
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In this study, a new inversion method is presented for performing two-dimensional (2D) Fourier transform. The discretization of the continuous Fourier spectra is given by a series expansion with the scaled Hermite functions as square-integrable set of basis functions. The expansion coefficients are determined by solving an overdetermined inverse problem. In order to define a quick algorithm in calculating the Jacobian matrix of the problem, the special feature that the Hermite functions are eigenfunctions of the Fourier transformation is used. In the field of inverse problem theory, there are numerous procedures for noise rejection, so if the Fourier transformation is formulated as an inverse problem, these tools can be used to reduce the noise sensitivity. It was demonstrated in many case studies that the use of Cauchy-Steiner weights could increase the noise rejection capability of geophysical inversion methods. Following this idea, the two-dimensional Fourier transform is formulated as an iteratively reweighted least squares (IRLS) problem using Cauchy-Steiner weights. The new procedure is numerically tested using synthetic data.

Fourier Transforms

Fourier Transforms
Author: Goran Nikolic
Publisher: BoD – Books on Demand
Total Pages: 264
Release: 2017-02-08
Genre: Mathematics
ISBN: 9535128930
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The main purpose of this book is to provide a modern review about recent advances in Fourier transforms as the most powerful analytical tool for high-tech application in electrical, electronic, and computer engineering, as well as Fourier transform spectral techniques with a wide range of biological, biomedical, biotechnological, pharmaceutical, and nanotechnological applications. The confluence of Fourier transform methods with high tech opens new opportunities for detection and handling of atoms and molecules using nanodevices, with potential for a large variety of scientific and technological applications.

Noise Reduction in Speech Applications

Noise Reduction in Speech Applications
Author: Gillian M. Davis
Publisher: CRC Press
Total Pages: 342
Release: 2018-10-03
Genre: Technology & Engineering
ISBN: 1351835998
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Noise and distortion that degrade the quality of speech signals can come from any number of sources. The technology and techniques for dealing with noise are almost as numerous, but it is only recently, with the development of inexpensive digital signal processing hardware, that the implementation of the technology has become practical. Noise Reduction in Speech Applications provides a comprehensive introduction to modern techniques for removing or reducing background noise from a range of speech-related applications. Self-contained, it starts with a tutorial-style chapter of background material, then focuses on system aspects, digital algorithms, and implementation. The final section explores a variety of applications and demonstrates to potential users of the technology the results possible with the noise reduction techniques presented. The book offers chapters contributed by international experts, a practical, systems approach, and numerous references. For electrical, acoustics, signal processing, communications, and bioengineers, Noise Reduction in Speech Applications is a valuable resource that shows you how to decide whether noise reduction will solve problems in your own systems and how to make the best use of the technologies available.

Biophysics

Biophysics
Author: Mark C. Leake
Publisher: CRC Press
Total Pages: 457
Release: 2023-12-12
Genre: Medical
ISBN: 100380652X
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Biophysics: Tools and Techniques for the Physics of Life covers the experimental, theoretical, and computational tools and techniques of biophysics. It addresses the purpose, science, and application of all physical science instrumentation, theoretical analysis, and biophysical computational methods used in current research labs. The book first presents the historical background, concepts, and motivation for using a physical science toolbox to understand biology. It then familiarizes undergraduate students from the physical sciences with essential biological knowledge. The text subsequently focuses on experimental biophysical techniques that primarily detect biological components or measure/control biological forces. The author describes the science and application of key tools used in imaging, detection, general quantitation, and biomolecular interaction studies, which span multiple length and time scales of biological processes both in the test tube and in the living organism. Moving on to theoretical and computational biophysics tools, the book presents analytical mathematical methods and numerical simulation approaches for tackling challenging biological questions including exam-style questions at the end of each chapter as well as step-by-step solved exercises. It concludes with a discussion of the future of this exciting field. Future innovators will need to be trained in multidisciplinary science to be successful in industry, academia, and government support agencies. Addressing this challenge, this textbook educates future leaders on the development and application of novel physical science approaches to solve complex problems linked to biological questions. Features: Provides the full, modern physical science toolbox of experimental, theoretical, and computational techniques, such as bulk ensemble methods, single-molecule tools, live-cell and test tube methods, pencil-on-paper theory approaches, and simulations. Incorporates worked examples for the most popular physical science tools by providing full diagrams and a summary of the science involved in the application of the tool. Reinforces the understanding of key concepts and biological questions. A solutions manual is available upon qualifying course adoption.

A Wavelet Tour of Signal Processing

A Wavelet Tour of Signal Processing
Author: Stephane Mallat
Publisher: Elsevier
Total Pages: 663
Release: 1999-09-14
Genre: Computers
ISBN: 0080520839
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This book is intended to serve as an invaluable reference for anyone concerned with the application of wavelets to signal processing. It has evolved from material used to teach "wavelet signal processing" courses in electrical engineering departments at Massachusetts Institute of Technology and Tel Aviv University, as well as applied mathematics departments at the Courant Institute of New York University and École Polytechnique in Paris. Provides a broad perspective on the principles and applications of transient signal processing with wavelets Emphasizes intuitive understanding, while providing the mathematical foundations and description of fast algorithms Numerous examples of real applications to noise removal, deconvolution, audio and image compression, singularity and edge detection, multifractal analysis, and time-varying frequency measurements Algorithms and numerical examples are implemented in Wavelab, which is a Matlab toolbox freely available over the Internet Content is accessible on several level of complexity, depending on the individual reader's needs New to the Second Edition Optical flow calculation and video compression algorithms Image models with bounded variation functions Bayes and Minimax theories for signal estimation 200 pages rewritten and most illustrations redrawn More problems and topics for a graduate course in wavelet signal processing, in engineering and applied mathematics

Optimum Methods in Statistics

Optimum Methods in Statistics
Author: Ferenc Steiner
Publisher: Akademiai Kiads
Total Pages: 380
Release: 1997
Genre: Mathematics
ISBN:
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Practitioners of different disciplines often have a jungle of erroneous data which unfortunately contain only latently the necessary, immediately usable information. If a suitable model is chosen, the E(i) values calculated by the "best" model parameters are possibly near the primarily given x(i) data which are the raw material of the statistics. The optimum methods of statistics minimize the deviations on the basis of some principle: that of the "least squares" has been generally used for two centuries but statistical procedures based on it work effectively only if the distribution type of the errors is Gaussian or near to it. Since some years, however, global optimums can be economically calculated for whichever functions, consequently the principle of "minimum products" and that of "maximum reciprocals" can also be used both resulting in most frequent value (MFV) procedures which are outlier resistant and their statistical efficiencies have high values in a wide range of error distribution types, i.e., they can extract the information effectively from the primarily given data. The definition and characterization of new norms (besides the old L(2) one) is therefore unavoidable.

Biometrics: Concepts, Methodologies, Tools, and Applications

Biometrics: Concepts, Methodologies, Tools, and Applications
Author: Management Association, Information Resources
Publisher: IGI Global
Total Pages: 1887
Release: 2016-08-30
Genre: Social Science
ISBN: 1522509844
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Security and authentication issues are surging to the forefront of the research realm in global society. As technology continues to evolve, individuals are finding it easier to infiltrate various forums and facilities where they can illegally obtain information and access. By implementing biometric authentications to these forums, users are able to prevent attacks on their privacy and security. Biometrics: Concepts, Methodologies, Tools, and Applications is a multi-volume publication highlighting critical topics related to access control, user identification, and surveillance technologies. Featuring emergent research on the issues and challenges in security and privacy, various forms of user authentication, biometric applications to image processing and computer vision, and security applications within the field, this publication is an ideal reference source for researchers, engineers, technology developers, students, and security specialists.

Cumulated Index Medicus

Cumulated Index Medicus
Author:
Publisher:
Total Pages: 1416
Release: 1989
Genre: Medicine
ISBN:
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Signal Processing and Performance Analysis for Imaging Systems

Signal Processing and Performance Analysis for Imaging Systems
Author: S. Susan Young
Publisher: Artech House
Total Pages: 323
Release: 2008
Genre: Computers
ISBN: 1596932880
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This book presents today's most powerful signal processing techniques together with methods for assessing imaging system performance when each of these techniques is applied. This multi-use book helps you make the most of sensor hardware through software enhancement, and evaluate system and algorithm performance. You also learn how to make the best hardware/software decisions in developing the next-generation of image acquisition and analysis systems.