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Author:   M. Bertero (University of Genova, Italy) ,  P. Boccacci (University of Genova, Italy) ,  P. Boccacci (both of University of Genova, Italy)
Publisher:   Taylor & Francis Ltd
Imprint:   Institute of Physics Publishing
Dimensions:   Width: 15.60cm , Height: 1.90cm , Length: 23.40cm
Weight:   0.544kg
ISBN:  

9780750304351

ISBN 10:   0750304359
Pages:   352
Publication Date:   01 January 1998
Audience:   College/higher education ,  Undergraduate
Replaced By:   9780367467869
Format:   Paperback
Publisher's Status:   Unknown
Availability:   Out of print, replaced by POD  
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Table of Contents

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 The global point spread function 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 SVD of the Radon transform 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 COMMENTS AND CONCLUDING REMARKS 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 Minimization of quadratic functionals Contraction and non-expansive mappings The EM method References

Reviews

This is an essential book for all those interested imaging systems and the image derived from them ... I would like to take this opportunity to congratulate the authors on an excellent publication which should find a wide audience in an area of application mathematics that is becoming increasingly important. Jonathan Blackledge, Mathematics Today Although this valuable book is both an introduction into a modern field and instruction for the solution of difficult identification problems in imaging and metrology. It can be recommended to all students, scientists and engineers who are interested in the state of the art of solving inverse problems or who are practically dealing with modern approaches of image processing such as active vision. Optics and Laser Technology s an essential book for all those interested imaging systems and the image derived from them ... I would like to take this opportunity to congratulate the authors on an excellent publication which should find a wide audience in an area of application mathematics that is becoming increasingly important. Jonathan Blackledge, Mathematics Today Although this valuable book is both an introduction into a modern field and instruction for the solution of difficult identification problems in imaging and metrology. It can be recommended to all students, scientists and engineers who are interested in the state of the art of solving inverse problems or who are practically dealing with modern approaches of image processing such as active vision. Optics and Laser Technology

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