DC 7-Tensor decomposition with group invariance

Project Title: Tensor decomposition with group invariance
Advisors: H. Munthe-Kaas (UiT), C. Riener (UiT), E. Hubert (Inria), Mentor: Florian Strohl (UiT)
Objectives: The so called orbit recovery problem is the problem of recovering a planted signal from noisy measurements under unknown group actions. More concretely, one tries to recover the unknown vector from an observation which is distorted with some Gaussian noise and further transformed by a randomly drawn element from a compact group. This rather general setup covers many classical problems, for example, the discrete multireference alignment problem but also captures a wide array of practically relevant problems, for example in cryoelectron microscopy. The goal of the project will be to combine methods from invariant theory with semidefinite programming approaches to arrive at robust, reliable and more efficient algorithms for instances of this class of problems. Furthermore, we aim to bring our approaches to use in concrete examples stemming from structural biology and molecular chemistry. To this end we will have a collaboration with Florian Strohl who is the PI in the Optical System Development lab at UiT.
Expected Results: Design of a new, robust, reliable and more efficient algorithm for orbit recovery based on semidefinite optimisation with applications to concrete examples arising in Lightsheet Microscopy. Three scientific reports submitted for publication.
Planned secondment(s): A planned secondment at Inria (M13-24) to collaborate with Evelyne Hubert
Joint degree: UiT The Arctic University of Norway, Université Côte d’Azur

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