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Author: Carlo Ciulla
Publisher:
ISBN: 9781612330136
Category :
Languages : en
Pages : 328
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Book Description
This book discusses signal interpolation: specifically, it describes a special theory on the improvement of the approximation properties of mathematical functions. This text is intended for undergraduate and graduate students in colleges and universities. Students will learn that given an interpolation function (interpolator), a special theory exists which derives the transfer function directly from the math form of the interpolator, avoiding the bias in the approximation, of which the interpolation error is measure, and the arbitration in the choice of the math form of the transfer function. The transfer function is the function needed from the interpolation function in order to convolve the signal and to obtain the estimate of the signal at unknown locations. Along this process, two new classes of interpolation functions are derived from the original interpolator, and one more interpolation function is also derived which combines the two of them on a pixel wise basis. The capability of the special theory in determining the transfer function from the math form of the interpolator is new, and is not found in similar available textbooks, making this volume valuable to students studying signal interpolation.
Author: Carlo Ciulla
Publisher:
ISBN: 9781612330136
Category :
Languages : en
Pages : 328
Get Book Here
Book Description
This book discusses signal interpolation: specifically, it describes a special theory on the improvement of the approximation properties of mathematical functions. This text is intended for undergraduate and graduate students in colleges and universities. Students will learn that given an interpolation function (interpolator), a special theory exists which derives the transfer function directly from the math form of the interpolator, avoiding the bias in the approximation, of which the interpolation error is measure, and the arbitration in the choice of the math form of the transfer function. The transfer function is the function needed from the interpolation function in order to convolve the signal and to obtain the estimate of the signal at unknown locations. Along this process, two new classes of interpolation functions are derived from the original interpolator, and one more interpolation function is also derived which combines the two of them on a pixel wise basis. The capability of the special theory in determining the transfer function from the math form of the interpolator is new, and is not found in similar available textbooks, making this volume valuable to students studying signal interpolation.
Author: Carlo Ciulla
Publisher: Createspace Independent Pub
ISBN: 9781477567487
Category : Mathematics
Languages : en
Pages : 336
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Book Description
This research monograph has the following main theme. Given an interpolation function, which is supposed to determine an estimate of the unknown signal value, the reader can use the traditional approach (traditional interpolation function) to estimate the numerical value of the signal. Alternatively, the reader can follow the theoretical developments offered in the book and so design, on the basis of the unified theory described in the book, three new interpolation functions with improved approximation capabilities. That means, that under the unified theory, the book offers three new classes of interpolation functions with improved approximation capabilities of the true and unknown signal to estimate. These works were published in the year 2011 and submitted for peer review and they are now presented to the public through this new publication. There are likely to be three main types of readership of this research monograph. The primary readership is composed of users of libraries which may adopt the book as reference. The secondary readership is composed of the population of instructors/professors of a course in one of applied mathematics, signal-image interpolation, signal-image processing, biomedical imaging and/or biomedical engineering academic disciplines. In such case, the book can be used as an additional educational resource to be available both to undergraduate and graduate students, in order to assign homework and/or projects to be included in the coursework. The tertiary readership is composed of apprentices and/or passionate of math. In such case, the book would be used to employ time while following the desire of intellectual enrichment. The apprentices and/or passionate of math would study the methodology of the unified theory, would apply the unified theory such to design new interpolation functions, and should there be the desire of furthering the interest, the apprentice and/or passionate would proceed further to the analysis of the results, and possibly into the discussion and the dissemination of the knowledge made out of this book.
Author: Ciulla, Carlo
Publisher: IGI Global
ISBN: 1605662038
Category : Computers
Languages : en
Pages : 640
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Book Description
"This book presents novel concepts supported through mathematics to create unique theories related to interpolation"--Provided by publisher.
Author: Carlo Ciulla
Publisher: Createspace Independent Publishing Platform
ISBN: 9781534708594
Category :
Languages : en
Pages : 176
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Book Description
The calculation of the intensity-curvature terms is related to the discrete sample of signal values and is also related to the analog/continuous transformation necessary to the function to become an interpolator. Such calculation is undertaken within the entire spatial extent of the sampling location, and as shown in Ciulla (2009), leads to the measurement of the energy level change determined through the interpolation function which is called: the Intensity-Curvature Functional. The idea is therefore to equate the intensity-curvature term calculated with the signal (image) through the given mathematical function in two conditions: (i) the given signal as it has been sampled and (ii) the signal calculated at locations where is unknown because of the limitations of the sampling instrument. Through mathematical developments that illustrate concepts of algebra and calculus, the equation of the two intensity-curvature terms furnish the instrument apt for deriving a new signal. This new signal is dependent on the given model function and is called Signal Resilient to Interpolation (SRI). The book includes illustration of the math processes, logical reasoning, which show how to generate the Signal Resilient to Interpolation. Within the book, the Signal Resilient to Interpolation is derived on the basis of quadratic and cubic polynomials in one, two and three dimensions, embedding and not embedding the pixel (voxel in three dimensions) to be re-sampled. Once the signal is modeled through an interpolator, it is possible to calculate the second order derivatives, and thus the curvature of the model interpolator which is nonetheless the modeled representation of the curvature of the signal. Geometrically, the curvature of the signal is the tangent to the first order derivative curve of the signal. There are two types of curvature treated in this book and they are: (i) classic-curvature and (ii) resilient curvature.
Author: Ronald E. Crochiere
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: Phillip A. Laplante
Publisher: CRC Press
ISBN: 1351032739
Category : Technology & Engineering
Languages : en
Pages : 856
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Book Description
The Encyclopedia of Image Processing presents a vast collection of well-written articles covering image processing fundamentals (e.g. color theory, fuzzy sets, cryptography) and applications (e.g. geographic information systems, traffic analysis, forgery detection). Image processing advances have enabled many applications in healthcare, avionics, robotics, natural resource discovery, and defense, which makes this text a key asset for both academic and industrial libraries and applied scientists and engineers working in any field that utilizes image processing. Written by experts from both academia and industry, it is structured using the ACM Computing Classification System (CCS) first published in 1988, but most recently updated in 2012.
Author: Ahmet H. Kayran
Publisher:
ISBN:
Category :
Languages : en
Pages : 126
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Book Description
Author: Joseph Charles Wheeler
Publisher:
ISBN:
Category : Digital electronics
Languages : en
Pages : 380
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Book Description
Author: Amir Z. Averbuch
Publisher: Springer Science & Business Media
ISBN: 9401789266
Category : Technology & Engineering
Languages : en
Pages : 514
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Book Description
This volume provides universal methodologies accompanied by Matlab software to manipulate numerous signal and image processing applications. It is done with discrete and polynomial periodic splines. Various contributions of splines to signal and image processing from a unified perspective are presented. This presentation is based on Zak transform and on Spline Harmonic Analysis (SHA) methodology. SHA combines approximation capabilities of splines with the computational efficiency of the Fast Fourier transform. SHA reduces the design of different spline types such as splines, spline wavelets (SW), wavelet frames (SWF) and wavelet packets (SWP) and their manipulations by simple operations. Digital filters, produced by wavelets design process, give birth to subdivision schemes. Subdivision schemes enable to perform fast explicit computation of splines' values at dyadic and triadic rational points. This is used for signals and images up sampling. In addition to the design of a diverse library of splines, SW, SWP and SWF, this book describes their applications to practical problems. The applications include up sampling, image denoising, recovery from blurred images, hydro-acoustic target detection, to name a few. The SWF are utilized for image restoration that was degraded by noise, blurring and loss of significant number of pixels. The book is accompanied by Matlab based software that demonstrates and implements all the presented algorithms. The book combines extensive theoretical exposure with detailed description of algorithms, applications and software. The Matlab software can be downloaded from http://extras.springer.com
Author: Jaakko Astola
Publisher: Hindawi Publishing Corporation
ISBN: 9775945550
Category : Electronic books
Languages : en
Pages : 425
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Book Description
"Digital signal transforms are of a fundamental value in digital signal and image processing. Their role is manifold. Transforms selected appropriately enable substantial compressing signals and images for storage and transmission. No signal recovery, image reconstruction and restoration task can be efficiently solved without using digital signal transforms. Transforms are successfully used for logic design and digital data encryption. Fast transforms are the main tools for acceleration of computations in digital signal and image processing. The volume collects in one book most recent developments in the theory and practice of the design and usage of transforms in digital signal and image processing. It emerged from the series of reports published by Tampere International Centre for Signal Processing, Tampere University of Technology. For the volume, all contributions are appropriately updated to represent the state of the art in the field and to cover the most recent developments in different aspects of the theory and applications of transforms. The book consists of two parts that represent two major directions in the field: development of new transforms and development of transform based signal and image processing algorithms. The first part contains four chapters devoted to recent advances in transforms for image compression and switching and logic design and to new fast transforms for digital holography and tomography. In the second part, advanced transform based signal and image algorithms are considered: signal and image local adaptive restoration methods and two complementing families of signal and image re-sampling algorithms, fast transform based discrete sinc-interpolation and spline theory based ones."--Publisher.
