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Author: M. B. Katz
Publisher: Springer Science & Business Media
ISBN: 3642455077
Category : Mathematics
Languages : en
Pages : 188
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Book Description
Reconstruction from projections has revolutionized radiology and has now become one of the most important tools of medical diagnosis The E. M. I. Scanner is one example. In this text, some fundamental theoretical and practical questions are resolved. Despite recent research activity in the area, the crucial subject of the uniqueness of the reconstruction and the effect of noise in the data posed some unsettled fundamental questions. In particular, Kennan Smith proved that if we describe an object by a C^inf_o function, i.e., infinitely differentiable with compact support, then there are other objects with the same shape, i.e., support, which can differ almost arbitrarily and still have the same projections in finitely many directions. On the other hand, he proved that objects in finite dimensional function spaces are uniquely determined by a single projection for almost all angles, i.e., except on a set of measure zero. Along these lines, Herman and Rowland in "Three Methods for reconstructing objects from x-rays: a comparative study" (1973) showed that reconstructions obtained from the commonly used algorithms can grossly misrepresent the object and that the algorithm which produced the best reconstruction when using noiseless data gave unsatisfactory results with noisy data. Equally important are reports in Science, and personal communications by radiologists indicating that in medical practice failure rates of reconstruction vary from four to twenty percent. within this work, the mathematical dilemma posed by Kennan Smith's result is discussed and clarified.
Author: M. B. Katz
Publisher: Springer Science & Business Media
ISBN: 3642455077
Category : Mathematics
Languages : en
Pages : 188
Get Book Here
Book Description
Reconstruction from projections has revolutionized radiology and has now become one of the most important tools of medical diagnosis The E. M. I. Scanner is one example. In this text, some fundamental theoretical and practical questions are resolved. Despite recent research activity in the area, the crucial subject of the uniqueness of the reconstruction and the effect of noise in the data posed some unsettled fundamental questions. In particular, Kennan Smith proved that if we describe an object by a C^inf_o function, i.e., infinitely differentiable with compact support, then there are other objects with the same shape, i.e., support, which can differ almost arbitrarily and still have the same projections in finitely many directions. On the other hand, he proved that objects in finite dimensional function spaces are uniquely determined by a single projection for almost all angles, i.e., except on a set of measure zero. Along these lines, Herman and Rowland in "Three Methods for reconstructing objects from x-rays: a comparative study" (1973) showed that reconstructions obtained from the commonly used algorithms can grossly misrepresent the object and that the algorithm which produced the best reconstruction when using noiseless data gave unsatisfactory results with noisy data. Equally important are reports in Science, and personal communications by radiologists indicating that in medical practice failure rates of reconstruction vary from four to twenty percent. within this work, the mathematical dilemma posed by Kennan Smith's result is discussed and clarified.
Author: Myron Bernard Katz
Publisher:
ISBN:
Category : Image transmission
Languages : en
Pages : 338
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Book Description
Author: V. P. Golubyatnikov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311092031X
Category : Mathematics
Languages : en
Pages : 132
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Book Description
The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Author: Eric Andres
Publisher: Springer Science & Business Media
ISBN: 3540255133
Category : Computers
Languages : en
Pages : 438
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Book Description
This book constitutes the refereed proceedings of the 12th International Conference on Discrete Geometry for Computer Imagery, DGCI 2005, held in Poitiers, France in April 2005. The 36 revised full papers presented together with an invited paper were carefully reviewed and selected from 53 submissions. The papers are organized in topical sections on applications, discrete hierarchical geometry, discrete tomography, discrete topology, object properties, reconstruction and recognition, uncertain geometry, and visualization.
Author: M B Katz
Publisher:
ISBN: 9783642455087
Category :
Languages : en
Pages : 194
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Book Description
Author: Ei Teramoto
Publisher: Springer Science & Business Media
ISBN: 3642933602
Category : Mathematics
Languages : en
Pages : 359
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Book Description
This volume represents the edited proceedings of the International Symposium on Mathematical Biology held in Kyoto, November 10-15, 1985. The symposium was or ganized by an international committee whose members are: E. Teramoto, M. Yamaguti, S. Amari, S.A. Levin, H. Matsuda, A. Okubo, L.M. Ricciardi, R. Rosen, and L.A. Segel. The symposium included technical sessions with a total of 11 invited papers, 49 contributed papers and a poster session where 40 papers were displayed. These Proceedings consist of selected papers from this symposium. This symposium was the second Kyoto meeting on mathematical topics in biology. The first was held in conjunction with the Sixth International Biophysics Congress in 1978. Since then this field of science has grown enormously, and the number of scientists in the field has rapidly increased. This is also the case in Japan. About 80 young japanese scientists and graduate students participated this time. . The sessions were divided into 4 ; , categories: 1) Mathematical Ecology and Population Biology, 2) Mathematical Theory of Developmental Biology and Morphogenesis, 3) Theoretical Neurosciences, and 4) Cell Kinetics and Other Topics. In every session, there were stimulating and active discussions among the participants. We are convinced that the symposium was highly successful in transmitting scientific information across disciplines and in establishing fruitful contacts among the participants. We owe this success to the cooperation of all participants.
Author: Carlos Castillo-Chavez
Publisher: Springer Science & Business Media
ISBN: 3642466931
Category : Mathematics
Languages : en
Pages : 340
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Book Description
Increasingly, mathematical methods are being used to advantage in addressing the problems facing humanity in managing its environment. Problems in resource management and epidemiology especially have demonstrated the utility of quantitative modeling. To explore these approaches, the Center of Applied Mathematics at Cornell University organized a conference in Fall, 1987, with the objective of surveying and assessing the state of the art. This volume records the proceedings of that conference. Underlying virtually all of these studies are models of population growth, from individual cells to large vertebrates. Cell population growth presents the simplest of systems for study, and is of fundamental importance in its own right for a variety of medical and environmental applications. In Part I of this volume, Michael Shuler describes computer models of individual cells and cell populations, and Frank Hoppensteadt discusses the synchronization of bacterial culture growth. Together, these provide a valuable introduction to mathematical cell biology.
Author: Myron Katz
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 208
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Book Description
Author: Henry Stark
Publisher: Elsevier
ISBN: 0323145973
Category : Technology & Engineering
Languages : en
Pages : 565
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Book Description
Image Recovery: Theory and Application focuses on signal recovery and synthesis problems. This book discusses the concepts of image recovery, including regularization, the projection theorem, and the pseudoinverse operator. Comprised of 13 chapters, this volume begins with a review of the basic properties of linear vector spaces and associated operators, followed by a discussion on the Gerchberg-Papoulis algorithm. It then explores image restoration and the basic mathematical theory in image restoration problems. The reader is also introduced to the problem of obtaining artifact-free computed tomographic reconstruction. Other chapters consider the importance of Bayesian approach in the context of medical imaging. In addition, the book discusses the linear programming method, which is particularly important for images with large number of pixels with zero value. Such images are usually found in medical imaging, microscopy, electron microscopy, and astronomy. This book can be a valuable resource to materials scientists, engineers, computed tomography technologists, and astronomers.
Author: Jean-Pierre Gabriel
Publisher: Springer
ISBN: 3662100673
Category : Mathematics
Languages : en
Pages : 208
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Book Description
This collection of papers gives a representative cross-selectional view of recent developments in the field. After a survey paper by C. Lefèvre, 17 other research papers look at stochastic modeling of epidemics, both from a theoretical and a statistical point of view. Some look more specifically at a particular disease such as AIDS, malaria, schistosomiasis and diabetes.
