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Details of Grant 

EPSRC Reference: EP/X010740/1
Title: Stochastic Gradient Descent in Banach Spaces
Principal Investigator: Kereta, Dr Z
Other Investigators:
Researcher Co-Investigators:
Project Partners:
University of Genoa University of Graz
Department: Computer Science
Organisation: UCL
Scheme: EPSRC Fellowship
Starts: 01 June 2023 Ends: 31 May 2026 Value (£): 348,066
EPSRC Research Topic Classifications:
Numerical Analysis
EPSRC Industrial Sector Classifications:
No relevance to Underpinning Sectors
Related Grants:
Panel History:
Panel DatePanel NameOutcome
24 Jan 2023 EPSRC Mathematical Sciences Fellowship Interview January 2023 Announced
01 Nov 2022 EPSRC Mathematical Sciences Prioritisation Panel November 2022 Announced
Summary on Grant Application Form
Inverse problems are concerned with the reconstruction of the causes of a physical phenomena from given observational data. They have wide applications in many problems in science and engineering such as medical imaging, signal processing, and machine learning. Iterative methods are a particularly powerful paradigm for solving a wide variety of inverse problems. They are often posed by defining an objective function that contains information about data fidelity and assumptions about the sought quantity, which is then minimised through an iterative process. Mathematics has played a critical role in analysing inverse problems and corresponding algorithms.

Recent advances in data acquisition and precision have resulted in datasets of increasing size for a vast number of problems, including computed and positron emission tomography. This increase in data size poses significant computational challenges for traditional reconstruction methods, which typically require the use of all the observational data in each iteration. Stochastic iterative methods address this computational bottleneck by using only a small subset of observation in each iteration. The resulting methods are highly scalable, and have been successfully deployed in a wide range of problems. However, the use of stochastic methods has thus far been limited to a restrictive set of geometric assumptions, requiring Hilbert or Euclidean spaces.

The proposed fellowship aims to address these issues by developing stochastic gradient methods for solving inverse problems posed in Banach spaces. The use of non-Hilbert spaces is gaining increased attention within inverse problems and machine learning communities. Banach spaces offer much richer geometric structures, and are a natural problem domain for many problems in partial differential equation and medical tomography. Moreover, Banach-space norms are advantageous for preservation of important properties, such as sparsity. This fellowship will introduce modern optimisation methods into classical Banach space theory and its successful completion will create novel research opportunities for inverse problems and machine learning.

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