Startseite Mathematik Utilizing uncertainty quantification variational autoencoders in inverse problems with applications in photoacoustic tomography
Kapitel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Utilizing uncertainty quantification variational autoencoders in inverse problems with applications in photoacoustic tomography

  • Hwan Goh , Teemu Sahlström und Tanja Tarvainen
Veröffentlichen auch Sie bei De Gruyter Brill
Erkunden Sie dieses Fachgebiet So veröffentlichen Sie bei uns
Data-driven Models in Inverse Problems
Ein Kapitel aus dem Buch Data-driven Models in Inverse Problems

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.

Kapitel in diesem Buch

  1. Frontmatter I
  2. Preface V
  3. Contents VII
  4. Part I: Mathematical aspects of data-driven methods in inverse problems
  5. On optimal regularization parameters via bilevel learning 1
  6. Learned regularization for inverse problems 39
  7. Inverse problems with learned forward operators 73
  8. Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imaging 107
  9. Learned reconstruction methods for inverse problems: sample error estimates 163
  10. Statistical inverse learning problems with random observations 201
  11. General regularization in covariate shift adaptation 245
  12. Part II: Applications of data-driven methods in inverse problems
  13. Analysis of generalized iteratively regularized Landweber iterations driven by data 273
  14. Integration of model- and learning-based methods in image restoration 303
  15. Dynamic computerized tomography using inexact models and motion estimation 331
  16. Deep Bayesian inversion 359
  17. Utilizing uncertainty quantification variational autoencoders in inverse problems with applications in photoacoustic tomography 413
  18. Electrical impedance tomography: a fair comparative study on deep learning and analytic-based approaches 437
  19. Classification with neural networks with quadratic decision functions 471
  20. Index 495
https://doi.org/10.1515/9783111251233-012

Kapitel in diesem Buch

  1. Frontmatter I
  2. Preface V
  3. Contents VII
  4. Part I: Mathematical aspects of data-driven methods in inverse problems
  5. On optimal regularization parameters via bilevel learning 1
  6. Learned regularization for inverse problems 39
  7. Inverse problems with learned forward operators 73
  8. Unsupervised approaches based on optimal transport and convex analysis for inverse problems in imaging 107
  9. Learned reconstruction methods for inverse problems: sample error estimates 163
  10. Statistical inverse learning problems with random observations 201
  11. General regularization in covariate shift adaptation 245
  12. Part II: Applications of data-driven methods in inverse problems
  13. Analysis of generalized iteratively regularized Landweber iterations driven by data 273
  14. Integration of model- and learning-based methods in image restoration 303
  15. Dynamic computerized tomography using inexact models and motion estimation 331
  16. Deep Bayesian inversion 359
  17. Utilizing uncertainty quantification variational autoencoders in inverse problems with applications in photoacoustic tomography 413
  18. Electrical impedance tomography: a fair comparative study on deep learning and analytic-based approaches 437
  19. Classification with neural networks with quadratic decision functions 471
  20. Index 495
Jetzt anmelden und 20% sparen
Institutioneller Zugang
Wie funktioniert Authentifizierung?
Haben Sie eine Idee, wie wir unsere Website verbessern können?
Bitte schreiben Sie uns.
© 2025 De Gruyter Brill
Heruntergeladen am 12.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/9783111251233-012/html?lang=de
Button zum nach oben scrollen