Deep neural networks for inverse problems with pseudodifferential operators: an application to limited-angle tomography
Luca Ratti - University of Helsinki
I will present a novel convolutional neural network designed for learning pseudodifferential operators in the context of linear inverse problems. Such a network is able to replicate and outperform the results of the Iterative Soft Thresholding Algorithm (ISTA), a well-known reconstruction algorithm in sparsity-promoting minimization problems. By a combination of techniques and tools from regularization theory of inverse problems, multi-resolution wavelet analysis, and the theory of pseudodifferential operators, we are able to theoretically deduce the architecture of the network and to prove its convergence properties. Our case study is limited-angle computed tomography: we test two different implementations of our network on simulated data from limited-angle geometry, achieving noteworthy preliminary results. This is a joint project with T. A. Bubba, M. Lassas, S. Siltanen from University of Helsinki and M. Galinier, M. Prato from Università di Modena.
I got my Ph.D. at Politecnico di Milano in February 2019. Since March 2019 I have been a post-doc researcher in the Inverse Problems group at the University of Helsinki. My research focuses on inverse problems related to (nonlinear) PDEs, optimization, and combining regularization theory with machine learning approaches.
2020-07-14 at 3:00 pm