Utilizing uncertainty quantification variational autoencoders in inverse problems with applications in photoacoustic tomography
-
Hwan Goh
Abstract
There is an increasing interest in utilizing machine learning methods in image processing and inverse problems. A significant part of the current work in inverse problems has, however, concentrated on image reconstruction problems, and the number of studies regarding estimating the posterior distribution in the context of Bayesian inverse problems has been limited. In this chapter, we study a machine learning-based approach for estimating the posterior distribution utilizing variational autoencoders, and a recently proposed uncertainty quantification variational autoencoder. The methodology is studied with numerical simulations with applications in photoacoustic tomography, where one aims at estimating a conditional probability distribution of an initial pressure when photoacoustic pressure waves on the boundary of the target are given. The simulations show that the uncertainty quantification variational autoencoder can provide a computationally efficient method for estimating the unknown initial pressure and evaluating its reliability in photoacoustic tomography.
Abstract
There is an increasing interest in utilizing machine learning methods in image processing and inverse problems. A significant part of the current work in inverse problems has, however, concentrated on image reconstruction problems, and the number of studies regarding estimating the posterior distribution in the context of Bayesian inverse problems has been limited. In this chapter, we study a machine learning-based approach for estimating the posterior distribution utilizing variational autoencoders, and a recently proposed uncertainty quantification variational autoencoder. The methodology is studied with numerical simulations with applications in photoacoustic tomography, where one aims at estimating a conditional probability distribution of an initial pressure when photoacoustic pressure waves on the boundary of the target are given. The simulations show that the uncertainty quantification variational autoencoder can provide a computationally efficient method for estimating the unknown initial pressure and evaluating its reliability in photoacoustic tomography.
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
-
Part I: Mathematical aspects of data-driven methods in inverse problems
- On optimal regularization parameters via bilevel learning 1
- Learned regularization for inverse problems 39
- Inverse problems with learned forward operators 73
- Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imaging 107
- Learned reconstruction methods for inverse problems: sample error estimates 163
- Statistical inverse learning problems with random observations 201
- General regularization in covariate shift adaptation 245
-
Part II: Applications of data-driven methods in inverse problems
- Analysis of generalized iteratively regularized Landweber iterations driven by data 273
- Integration of model- and learning-based methods in image restoration 303
- Dynamic computerized tomography using inexact models and motion estimation 331
- Deep Bayesian inversion 359
- Utilizing uncertainty quantification variational autoencoders in inverse problems with applications in photoacoustic tomography 413
- Electrical impedance tomography: a fair comparative study on deep learning and analytic-based approaches 437
- Classification with neural networks with quadratic decision functions 471
- Index 495
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
-
Part I: Mathematical aspects of data-driven methods in inverse problems
- On optimal regularization parameters via bilevel learning 1
- Learned regularization for inverse problems 39
- Inverse problems with learned forward operators 73
- Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imaging 107
- Learned reconstruction methods for inverse problems: sample error estimates 163
- Statistical inverse learning problems with random observations 201
- General regularization in covariate shift adaptation 245
-
Part II: Applications of data-driven methods in inverse problems
- Analysis of generalized iteratively regularized Landweber iterations driven by data 273
- Integration of model- and learning-based methods in image restoration 303
- Dynamic computerized tomography using inexact models and motion estimation 331
- Deep Bayesian inversion 359
- Utilizing uncertainty quantification variational autoencoders in inverse problems with applications in photoacoustic tomography 413
- Electrical impedance tomography: a fair comparative study on deep learning and analytic-based approaches 437
- Classification with neural networks with quadratic decision functions 471
- Index 495
