A computational framework and implementation of implicit priors in Bayesian inverse problems

arXiv

This repository contains supplementary materials to our manuscript.

Notebooks

Pedagogical examples

• Simplest linear Bayesian inverse problem (Section 4.2-4.4), RLRTO
• Simplest nonlinear Bayesian inverse problem (Section 4.5), Langevin

Application case studies

• Deblurring with constraints (Section 5.1), RLRTO
• Various inverse problems with the Poisson equation (Section 5.2)
  • Source term 1 2 3, RLRTO
  • Boundary value, RLRTO
  • Conductivity together with comparing different TV regularization strength, Langevin
• Image inpainting (Section 5.3)
  • Wavelet denoiser, Langevin
  • DnCNN denoiser, Langevin

Environment

Core libraries being used and their respective versions:

• CUQIpy 1.3.0
• CUQIpy-FEniCS 0.8.0
• Scikit-image 0.23.2
• Deepinverse 0.3.0
• FEniCS 2019