Book contents
- Frontmatter
- Dedication
- Contents
- List of Contributors
- Preface
- Part I Theory of Deep Learning for Image Reconstruction
- 1 Formalizing Deep Neural Networks
- 2 Geometry of Deep Learning
- 3 Model-Based Reconstruction with Learning: From Unsupervised to Supervised and Beyond
- 4 Deep Algorithm Unrolling for Biomedical Imaging
- Part II Deep-Learning Architecture for Various Imaging Architectures
- Part III Generative Models for Biomedical Imaging
1 - Formalizing Deep Neural Networks
from Part I - Theory of Deep Learning for Image Reconstruction
Published online by Cambridge University Press: 15 September 2023
Book contents
- Frontmatter
- Dedication
- Contents
- List of Contributors
- Preface
- Part I Theory of Deep Learning for Image Reconstruction
- 1 Formalizing Deep Neural Networks
- 2 Geometry of Deep Learning
- 3 Model-Based Reconstruction with Learning: From Unsupervised to Supervised and Beyond
- 4 Deep Algorithm Unrolling for Biomedical Imaging
- Part II Deep-Learning Architecture for Various Imaging Architectures
- Part III Generative Models for Biomedical Imaging
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Summary
We provide a short, self-contained introduction to deep neural networks that is aimed at mathematically inclined readers. We promote the use of a vect--matrix formalism that is well suited to the compositional structure of these networks and that facilitates the derivation/description of the backpropagation algorithm. We present a detailed analysis of supervised learning for the two most common scenarios, (i) multivariate regression and (ii) classification, which rely on the minimization of least squares and cross-entropy criteria, respectively.
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- Deep Learning for Biomedical Image Reconstruction , pp. 3 - 12Publisher: Cambridge University PressPrint publication year: 2023
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