Inverse imaging with Poisson data : from cells to galaxies / Mario Bertero, Patrizia Boccacci, Valeria Ruggiero.

Format:

Book

Author/Creator:

Bertero, Mario, author.

Boccacci, Patrizia, author.

Ruggiero, Valeria, author.

Contributor:

Institute of Physics (Great Britain), publisher.

Series:

IOP (Series). Release 6.

IOP expanding physics

[IOP release 6]

IOP expanding physics, 2053-2563

Language:

English

Subjects (All):

Image processing--Mathematics.

Image processing.

Inverse problems (Differential equations).

Poisson distribution.

Physical Description:

1 online resource (various pagings) : illustrations (some color).

Place of Publication:

Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2018]

System Details:

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

text file

Biography/History:

Mario Bertero received an advanced degree in physics from the University of Genova in Italy in 1960, and he obtained the libera docenza in theoretical physics in 1968. He has professorships in mathematics and computer science and was the editor of Inverse Problems from 1990-1994. He has retired from teaching but not from research. Patrizia Boccacci received her advanced degree in physics from the University of Genova in Italy in 1980. She is currently an associate professor in the Department of Informatics, Bioengineering, Robotics and System Engineering at the University of Genova. Valeria Ruggiero received her advanced degree in mathematics from the University of Ferrara in Italy in 1978. She is a professor in numerical analysis at the University of Ferrara and is the director of the National Group for Scientific Computation of the Istituto Nazionale di Alta Matematica (INdAM).

Summary:

Inverse Imaging with Poisson Data is an invaluable resource for graduate students, postdocs and researchers interested in the application of inverse problems to the domains of applied sciences, such as microscopy, medical imaging and astronomy. The purpose of the book is to provide a comprehensive account of the theoretical results, methods and algorithms related to the problem of image reconstruction from Poisson data within the framework of the maximum likelihood approach introduced by Shepp and Vardi.

Contents:

1. Introduction

1.1. Scope of the book and topic selection

1.2. Structure of the book

2. Examples of applications

2.1. Fluorescence microscopy

2.2. Medical imaging (tomography)

2.3. Astronomy

3. Mathematical modeling

3.1. Imaging system and forward problem

3.2. Ill-posedness of the backward (inverse) problem

3.3. Detection and data sampling

3.4. Detection and data noise

3.5. The discrete models

3.6. Supplementary material

4. Statistical approaches in a discrete setting

4.1. Maximum likelihood approach and data-fidelity function

4.2. Bayesian regularization

4.3. Denoising problems

4.4. Selection of the regularization parameter

4.5. The Bregman iteration

4.6. Supplementary material

5. Simple reconstruction methods

5.1. Expectation maximization (EM) or Richardson-Lucy (RL) method

5.2. Ordered subset expectation maximization method

5.3. One-step late (OSL) method

5.4. Split gradient method (SGM)

5.5. Supplementary material

6. Optimization methods

6.1. Some basic tools : proximity operators and conjugate functions

6.2. The family of forward-backward (FB) splitting methods

6.3. FB methods for smooth problems of image reconstruction

6.4. FB methods for non-smooth problems of image reconstruction

6.5. The alternating direction method of multipliers (ADMM)

6.6. Primal-dual methods

6.7. Majorization-minimization approach

6.8. Towards non-convex minimization problems

7. Numerics

7.1. Semi-convergent methods

7.2. Methods for edge-preserving regularization

7.3. Image reconstruction of real data

8. Specific topics in image deblurring

8.1. Super-resolution by data inversion

8.2. Boundary artifacts correction

8.3. Blind deconvolution

8.4. Images with point and smooth sources

8.5. Images with space-variant blur

9. Towards a regularization theory

9.1. Deterministic regularization approaches

9.2. Statistical approaches

9.3. Comments and concluding remarks.

Notes:

"Version: 20181201"--Title page verso.

Includes bibliographical references.

Title from PDF title page (viewed on January 16, 2019).

Other Format:

Print version:

ISBN:

9780750314374

9780750314398

OCLC:

1082881981

Access Restriction:

Restricted for use by site license.