Research project: Structured low-rank approximation: Theory, algorithms, and applications
Today's state-of-the-art methods for data processing are model based. We propose a fundamentally new approach that does not depend on an explicit model representation and can be used for model-free data processing. From a theoretical point of view, the prime advantage of the newly proposed paradigm is conceptual unification of existing methods. From a practical point of view, the proposed paradigm opens new possibilities for development of computational methods for data processing. The underlying computational tool in the proposed setting is low-rank approximation. Recent work by the applicant, co-workers, and others has demonstrated advantages of computational methods based on low-rank approximation over classical methods, based on solution of linear systems of equations. In this proposal, we will further advance the theory and algorithms for low-rank approximation by developing robust and efficient local optimisation methods and methods based on convex relaxations.