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This book presents recent mathematical methods in the area of inverse problems in imaging with a particular focus on the computational aspects and applications. The formulation of inverse problems in imaging requires accurate mathematical modeling in order to preserve the significant features of the image. The book describes computational methods to efficiently address these problems based on new optimization algorithms for smooth and nonsmooth convex minimization, on the use of structured (numerical) linear algebra, and on multilevel techniques. It also discusses various current and challenging applications in fields such as astronomy, microscopy, and biomedical imaging. The book is intended for researchers and advanced graduate students interested in inverse problems and imaging.
List of contents
1 Silvia Bonettini et al., Recent advances in variable metric first-order methods.- 2 Davide Bianchi et al., Structure preserving preconditioning for frame-based image deblurring.- 3 Pietro Dell'Acqua et al, Non-stationary structure-preserving preconditioning for image restoration.- 4 Sean Hon and Andy Wathen, Numerical investigation of the spectral distribution of Toeplitz-function sequences.- 5 Anna Maria Massone et al., The Hough transform and the impact of chronic leukemia on the compact bone tissue from CT-images analysis.- 6 Marco Prato et al., Multiple image deblurring with high dynamic-range Poisson data.- 7 Silvia Tozza and Maurizio Falcone, On the segmentation of astronomical images via level-set methods.
About the author
Marco Donatelli is an Associate Professor of Numerical Analysis at the Department of Science and High Technology, University of Insubria (Italy). He was awarded a Ph.D. in Applied Mathematics by the University of Milan in 2006. His research interests include regularization methods of inverse problems, preconditioning and multigrid methods for structured matrices. He is author of more than 70 papers and he serves on the editorial boards of three international journals.
Stefano Serra-Capizzano is a Full Professor of Numerical Analysis at the Department of Humanities and Innovation, Deputy Rector of the University of Insubria (Italy) and long-term Visiting Scholar at Uppsala University (Sweden). He has authored over 200 research papers in different areas of mathematics, including numerical linear algebra, spectral theory, approximation theory, and inverse problems, with more than 100 collaborators around the globe. He is the founder of the Ph.D. Program "Mathematics of Computation" and of the Department of Science and High Technology at the University of Insubria.
