Learning and Experimental Design for Inverse Problems in Imaging

Christoph Brune*, Braxton Osting and Stanley Osher

This talk contributes to learning methods for inverse problems in imaging. Experimental design respectively optimal data collection for inverse problems in imaging often leads to bilevel and eigenvalue optimization problems with particular design and information criteria, e.g. Fisher information, mutual information or Gram matrices. We will study novel selection models for trajectory design applied to compressive sensing MRI and non-raster Atomic Force Microscopy and related optimization problems. Besides, the talk will address learning methods for sparse priors in variational image reconstruction models related to dictionary learning.

Mathematics Subject Classification: 49N45 68U10 94A08 94A15

Keywords: Experimental design; learning; bilevel optimization; inverse problems; image processing; sparsity

Minisymposion: Noise Estimation, Model Selection and Bilevel Optimization