# Introduction to Inverse Problems in Imaging

## Bertero, M.; Boccacci, P.

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This is a graduate textbook on the principles of linear inverse problems, methods of their approximate solution, and practical application in imaging. The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of readers from different backgrounds in science and engineering. Mathematical prerequisites are first courses in analysis, geometry, linear algebra, probability theory, and Fourier analysis. The authors concentrate on presenting easily implementable and fast solution algorithms. With examples and exercised throughout, the book will provide the reader with the appropriate background for a clear understanding of the essence of inverse problems (ill-posedness and its cure) and, consequently, for an intelligent assessment of the rapidly growing literature on these problems.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Contenuti:

INTRODUCTION
What is an inverse problem?
What is an ll-posed problem?
How to cure ill-posedness
An outline of the book
Reference

IMAGE DECONVOLUTION
SOME MATHEMATICAL TOOLS
The Fourier transform (FT)
Bandlimited functions and sampling theorems
Convolution operators
The discrete Fourier transform (DFT)
Cyclic matrices
Relationship between FT and DFT
Discretization of the convolution product
References

EXAMPLES OF IMAGE BLURRING
Blurring and noise
Linear motion blur
Out-of-focus blur
Diffraction-limited imaging systems
Atmospheric turbulence blur
Near-field acoustic holography
References

THE ILL-POSEDNESS OF IMAGE DECONVOLUTION
Formulation of the problem
Well-posed and ill-posed problems
Existence of the solution and inverse filtering
Discretization: from ill-posedness to ill-conditioning
Bandlimited systems: least-squares solutions and generalized solution Approximate solutions and the use of a priori information
Constrained least-squares
References

REGULARIZATION METHODS
Least squares solutions with prescribed energy
Approximate solutions with minimal energy
Regularization algorithms in the sense of Tikhonov
Regularization and filtering
Choice of the regularization parameter
References

ITERATIVE REGULARIZATION METHODS
The Landweber method
The projected Landweber method for the computation of constrained regularized solutions
The steepest descent and the conjugate gradient method
References

STATISTICAL METHODS
Maximum likelihood (ML) methods
The ML method in the case of Gaussian noise
The ML method in the case of Poisson noise
Bayesian methods
The Wiener filter
References

LINEAR INVERSE IMAGING PROBLEMS
EXAMPLES OF LINEAR INVERSE PROBLEMS
Space-variant imaging systems
X-ray tomography
Emission tomography
Inverse diffraction and inverse source problems
Linearized inverse scattering problems
References

SINGULAR VALUE DECOMPOSITION (SVD)
Mathematical description of linear imaging systems
SVD of a matrix
SVD of a semi-discrete mapping
SVD of an integral operator with square-integrable kernel
References

INVERSION METHODS REVISITED
The generalized solution
The Tikhonov regularization method
Truncated SVD
Iterative regularization methods
Statistical methods
References

FOURIER-BASED METHODS FOR SPECIFIC PROBLEMS
The Fourier slice theorem in tomography
The filtered backprojection (FBP) method in tomography
Implementation of the discrete FBP
Resolution and super-resolution in image restoration
Out-of-band extrapolation
The Gerchberg method and its generalization
References

Does there exist a general-purpose method?
In praise of simulation
References

MATHEMATICAL APPENDICES
Euclidean and Hilbert spaces of functions
Linear operators in function spaces
Euclidean vector spaces and matrices
Properties of the DFT and the FFT algorithm
Contraction and non-expansive mappings
The EM method
References

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## 1.Introduction To Inverse Problems In Imaging

ISBN 10: 0750304359 ISBN 13: 9780750304351
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## 2.Introduction to Inverse Problems in Imaging

Editore: CRC Press (1998)
ISBN 10: 0750304359 ISBN 13: 9780750304351
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Descrizione libro CRC Press, 1998. PAP. Condizione libro: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Codice libro della libreria F9-9780750304351

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## 3.Introduction to Inverse Problems in Imaging (Paperback)

Editore: Taylor Francis Ltd, United Kingdom (1998)
ISBN 10: 0750304359 ISBN 13: 9780750304351
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Descrizione libro Taylor Francis Ltd, United Kingdom, 1998. Paperback. Condizione libro: New. 231 x 157 mm. Language: English . Brand New Book ***** Print on Demand *****. This is a graduate textbook on the principles of linear inverse problems, methods of their approximate solution, and practical application in imaging. The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of readers from different backgrounds in science and engineering. Mathematical prerequisites are first courses in analysis, geometry, linear algebra, probability theory, and Fourier analysis. The authors concentrate on presenting easily implementable and fast solution algorithms. With examples and exercised throughout, the book will provide the reader with the appropriate background for a clear understanding of the essence of inverse problems (ill-posedness and its cure) and, consequently, for an intelligent assessment of the rapidly growing literature on these problems. Codice libro della libreria AAV9780750304351

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## 4.Introduction to Inverse Problems in Imaging (Paperback)

Editore: Taylor Francis Ltd, United Kingdom (1998)
ISBN 10: 0750304359 ISBN 13: 9780750304351
Nuovi Paperback Quantità: 10
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Descrizione libro Taylor Francis Ltd, United Kingdom, 1998. Paperback. Condizione libro: New. 231 x 157 mm. Language: English . Brand New Book ***** Print on Demand *****.This is a graduate textbook on the principles of linear inverse problems, methods of their approximate solution, and practical application in imaging. The level of mathematical treatment is kept as low as possible to make the book suitable for a wide range of readers from different backgrounds in science and engineering. Mathematical prerequisites are first courses in analysis, geometry, linear algebra, probability theory, and Fourier analysis. The authors concentrate on presenting easily implementable and fast solution algorithms. With examples and exercised throughout, the book will provide the reader with the appropriate background for a clear understanding of the essence of inverse problems (ill-posedness and its cure) and, consequently, for an intelligent assessment of the rapidly growing literature on these problems. Codice libro della libreria AAV9780750304351

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## 5.Introduction to Inverse Problems in Imaging

Editore: CRC Press (1998)
ISBN 10: 0750304359 ISBN 13: 9780750304351
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Descrizione libro CRC Press, 1998. PAP. Condizione libro: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria LQ-9780750304351

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## 6.Introduction to Inverse Problems in Imaging. Taylor & Francis. 1998.

Editore: Taylor & Francis (2017)
ISBN 10: 0750304359 ISBN 13: 9780750304351
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Descrizione libro Taylor & Francis, 2017. Paperback. Condizione libro: NEW. 9780750304351 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Print on Demand title, produced to the highest standard, and there would be a delay in dispatch of around 10 working days. Codice libro della libreria HTANDREE0247606

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## 7.Introduction to Inverse Problems in Imaging

Editore: Taylor & Francis US (2016)
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Descrizione libro Taylor & Francis US, 2016. Paperback. Condizione libro: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Codice libro della libreria ria9780750304351_lsuk

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## 8.Introduction to Inverse Problems in Imaging

Editore: CRC Press (1998)
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Descrizione libro CRC Press, 1998. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria IQ-9780750304351

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## 9.Introduction to Inverse Problems in Imaging

Editore: CRC Press (1998)
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Descrizione libro CRC Press, 1998. Paperback. Condizione libro: New. book. Codice libro della libreria 0750304359

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## 10.Introduction to Inverse Problems in Imaging

Editore: Inst of Physics Pub Inc (1998)
ISBN 10: 0750304359 ISBN 13: 9780750304351
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Descrizione libro Inst of Physics Pub Inc, 1998. Paperback. Condizione libro: Brand New. 1st edition. 352 pages. 9.25x6.25x0.75 inches. In Stock. Codice libro della libreria __0750304359

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