Abstract : In recent years, there has been an increasing interest in exploring how to combine the practical advantages of learning-based methods with the theoretical understanding and the convergence guarantees coming from model-based approaches for the regularisation of ill-posed inverse problems. This mini-symposium will bring together researchers working on data-driven methods and deep learning for inverse problems in the attempt to providing an overview of the mathematical insights able to shed light on how learned image reconstruction approaches can be reliable tools for real-world applications.
Organizer(s) : Tatiana A. Bubba, Luca Calatroni, Luca Ratti
[03849] Untrained networks with latent-space disentanglement for motion separation in videos
Format : Talk at Waseda University
Author(s) :
Malena Sabaté Landman (Department of Applied Mathematics and Theoretical Physics, University of Cambridge)
Abudllah Abudllah (Department of Mathematics, The Chinese University of Hong Kong)
Martin Holler (Institute of Mathematics and Scientific Computing, University of Graz)
Karl Kunisch (Institute of Mathematics and Scientific Computing, University of Graz)
Abstract : In this talk I will present an algorithm that allows to efficiently isolate different, highly non-linear motion types in video data, using untrained generator networks together with a specific technique for latent space disentanglement that uses minimal, one-dimensional information on some of the underlying dynamics.
[01569] Continuous Generative Neural Networks for Inverse Problems
Format : Talk at Waseda University
Author(s) :
Giovanni Alberti (University of Genoa)
Matteo Santacesaria (University of Genoa)
Silvia Sciutto (University of Genoa)
Abstract : We study Continuous Generative Neural Networks CGNNs, namely, generative models in the continuous setting. The architecture is inspired by DCGAN, with one fully connected layer, several convolutional layers and nonlinear activation functions. In the continuous L^2 setting, the dimensions of the spaces of each layer are replaced by the scales of a multiresolution analysis of a compactly supported wavelet. We present conditions on the convolutional filters and on the nonlinearity that guarantee that a CGNN is injective. This theory finds applications to inverse problems, and allows for deriving Lipschitz stability estimates for possibly nonlinear infinite-dimensional inverse problems with unknowns belonging to the manifold generated by a CGNN.
[02780] Learned proximal operators in accelerated unfolded methods with pseudodifferential operators
Format : Online Talk on Zoom
Author(s) :
Andrea Sebastiani (University of Bologna)
Tatiana Alessandra Bubba (University of Bath)
Luca Ratti (University of Genoa)
Subhadip Mukherjee (University of Bath)
Abstract : In recent years, hybrid reconstruction frameworks has been proposed by unfolding iterative methods and learning a suitable pseudodifferential correction on the part that can provably not be handled by model-based methods. In this talk, I will present a variant of this approach, where an accelerated iterative algorithm is unfolded and the proximal operator is replaced by a learned operators, as in the PnP framework. The numerical experiments on limited-angle CT achieve promising results.
[02946] Electrical impedance tomography, virtual X-rays, and stroke
Format : Talk at Waseda University
Author(s) :
Samuli Siltanen (University of Helsinki)
Abstract : A connection between Electrical Impedance Tomography (EIT) and X-ray tomography was found in (Greenleaf et al. 2018) using microlocal analysis. Fourier transform applied to the spectral parameter of Complex Geometric Optics solutions produces virtual X-ray projections, enabling a novel filtered back-projection type nonlinear reconstruction algorithm for EIT. This approach is called Virtual Hybrid Edge Detection. Machine learning can be used for classifying stroke (into ischemic and hemorrhagic) based on virtual X-ray profiles of the conductivity.
[03308] Beyond supervised learning in imaging: measurement-driven computational imaging
Format : Talk at Waseda University
Author(s) :
Julian Tachella (CNRS, ENSL)
Abstract : Most computational imaging algorithms rely either on hand-crafted prior models (total variation, wavelets) or on supervised learning with a ground truth dataset of references. The first approach generally obtains suboptimal reconstructions, whereas the latter is impractical in many scientific and medical imaging applications where ground-truth data is expensive or even impossible to obtain. In this talk, I will present recent algorithmic and theoretical advances in unsupervised learning for imaging inverse problems that overcome these limitations, by learning from noisy and incomplete measurement data alone and leveraging weak prior knowledge on the reconstructed image distribution, such as invariance to groups of transformations (rotations, translations, etc.) and low-dimensionality.
[03519] Deep Learning for Reconstruction in Nano CT
Format : Talk at Waseda University
Author(s) :
Alice Oberacker (Saarland University)
Anne Wald (Georg-August-Universität Göttingen)
Bernadette Hahn-Rigaud (Universität Stuttgart)
Tobias Kluth (Universität Bremen)
Johannes Leuschner (Universität Bremen)
Maximilian Schmidt (Universität Bremen)
Thomas Schuster (Saarland University)
Abstract : Tomographic X-ray imaging at the nano-scale helps reveal the structures of materials like alloys and biological tissue. However, environmental perturbances during data acquisition can cause motion between the object and scanner. To reduce noise in the back-projection, a learned version of the RESESOP-Kaczmarz method was investigated. The deep network was trained with simulated imaging data to unroll the iterative reconstruction process, allowing the network to learn the back-projected image after a fixed number of iterations.
[04062] Learning intrinsic shape representations via LBO spectra
Format : Talk at Waseda University
Author(s) :
serena morigi (University of Bologna)
Abstract : Neural fields are emerging as a new function representation paradigm for image processing, computer vision, computer graphics, and more. The intrinsic neural fields rely on a feature embedding based on the Laplace Beltrami Operator. We derive the embedding functions from the solution of graph Laplacian-based variational regularization problems. This allows to impose property which directly derived from the associated variational formulation. An efficient model-aware method as well as a model-blind neural network will be presented.
[04272] Inexact Algorithms for Bilevel Learning
Format : Talk at Waseda University
Author(s) :
Mohammad Sadegh Salehi (University of Bath)
Abstract : We consider hyperparameter estimation for variational methods formulated as a bilevel learning problem. Due to the use of numerical solvers, one can only compute an inexact gradient with respect to the hyperparameters. We introduce and analyse a new framework that dynamically updates the accuracy in inexact algorithms and selects stepsizes based on linesearch. We compare the performance of our method with existing methods through numerical experiments.
