Inverse imaging with Poisson data : from cells to galaxies /

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 a...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Bertero, Mario (Autor), Boccacci, Patrizia (Autor), Ruggiero, Valeria (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2018]
Colección:IOP (Series). Release 6.
IOP expanding physics.
Temas:
Image processing > Mathematics.
Inverse problems (Differential equations)
Poisson distribution.
Imaging systems & technology.
TECHNOLOGY & ENGINEERING / Imaging Systems.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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