Randomised Linear Algebra for Large Scale Inverse Problems at University of Edinburgh on FindAPhD.com

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Dr N Polydorides No more applications being accepted

About the Project

Applications are invited for a postgraduate research position leading to a PhD degree in Electrical Engineering in the Institute for Digital Communications within the School of Engineering at the University of Edinburgh.

Description: Recent advances in big data analytics have brought about various randomisation algorithms in the aim of exploring massive data sets and approximating linear algebra operations with matrices and vectors of massive dimensions. Among the most prominent examples of this innovation is the randomised singular value decomposition and randomised linear algebra algorithms for matrix multiplication and least squares regression. In principle, this new Monte-Carlo framework aims to replace high-dimensional deterministic computation with statistical estimation and sample-based averages, engaging selectively a few elements, rows, or columns of the matrices and vectors involved to approximate the result of a high-dimensional algebraic operation. The key element of this methodology is the choice of the sampling distribution so that the result is obtained quickly and with minimal statistical error. For ill-conditioned matrices, such as those encountered in the numerical solution of ill-posed inverse problems, randomisation methods can be very efficient, both in terms of estimation convergence, as well memory usage and the accuracy of the result.

This project is aimed at developing randomised algorithms for high-dimensional inverse problems associated with partial differential equations. The project will explore the design of efficient, low-variance sampling distributions based on importance sampling principles, and develop analytical and computational results to demonstrate the properties of these algorithms in the context of a high-dimensional computational imaging. The project is aimed at extending some initial work on sample-average approximations for large-scale linear inverse problems into a more generic framework for partial differential equations associated with electromagnetic imaging.

Keywords: Randomised linear algebra, inverse problems, Monte Carlo simulation, large-scale computing.

Funding Notes

Preferably a first class Honours degree (or International equivalent) in engineering, physics, informatics or applied mathematics, ideally supplemented by an MSc Degree. Solid background in signal processing and numerical computing, while previous experience in imaging sciences is desirable. Excellent writing and oral communication skills. Capability to work independently and used to take initiative and Programming skills are desirable.

Applications are welcomed from self-funded students, or students who are applying for scholarships from the University of Edinburgh or elsewhere.

References

The project will benefit from the interaction with a network of data scientists in computer science, mathematics and statistics, at the Alan Turing Institute as well as interaction with industrial collaborators in oil/gas industry.

Where will I study?

University of Edinburgh

One of the world''s top universities, consistently ranked in the world top 50 and placed 20th in the QS World University Rankings 2020. We provide a stimulating working, learning and teaching environment with access to excellent facilities and attract the world''s best, from Nobel Prize winning laureates to future explorers, pioneers and inventors.

Randomised Linear Algebra for Large Scale Inverse Problems

University of Edinburgh School of Engineering