Research Theme

Sensor Signal Processing

Aim

Develop new computationally efficient algorithms for large multi-dimensional array processing.

Objectives

1. Develop new fast beamforming algorithms and adaptive array processing techniques using advances in fast Fourier integral operators and randomized algorithms
2. Build applications using these techniques for high-dimensional wideband sensor array processing problems, e.g. requiring the simultaneous processing of range, doppler, azimuth, elevation and frequency, in challenging acoustic and/or radar domains.
3. Explore the performance trade-off between accuracy and computational efficiency.

Description

Large scale, multi-dimensional array processing problems, e.g. simultaneously processing range, doppler, azimuth, elevation and frequency, are ubiquitous in radar and sonar sensing, and it is essential to keep the computation to a minimum in order to process the outputs in a timely manner. For narrowband uniformly spaced linear arrays fast transforms such as the FFT can be exploited. However, dealing with large wideband non-uniform arrays remains a major challenge.

This project will develop novel fast array processing algorithms for statistical estimation and beamforming based on two recent developments in signal processing and related mathematics. The first is the construction of fast Fourier integral operator approximations [1,2,3,4], that can provably approximate the Fourier integral to a given level of accuracy in O(n.log(n)) while accommodating different sampling/physical geometries. The second is efficient fast randomized algorithms for solving large least square problems [5,6] that offer the potential for novel beamforming solutions [7]. The project will explore how these ideas can be integrated to develop novel efficient array processing solutions to tackle challenging sonar and RF array processing problems and to assess their performance trade-off between accuracy and computation.

[1] E. Candes, L. Demanet, & L. Ying, 2007, Fast Computation of Fourier Integral Operators. SIAM Journal on Scientific Computing, Vol. 29, Iss. 6, pp. 2464-2493. 

[2] L. Demanet, M. Ferrara, N. Maxwell, J. Poulson, and L. Ying, 2012, A butterfly algorithm for synthetic aperture radar imaging. SIAM J. Imag. Sci., vol. 5, no. 1, pp. 203–243.

[3] S. I. Kelly and M. E. Davies, 2014, A fast decimation-in-image back-projection algorithm for SAR. 2014 IEEE Radar Conference, pp. 1046-1051.

[4] S. I. Kelly, M. E. Davies, J. S. Thompson, 2014, Parallel Processing of the Fast Decimation-in-image Back-projection Algorithm for SAR. 2014 Sensor Signal Procesing for Defence (SSPD),  pp. 1-5.

[5] V. Rokhlin and M. Tygert, 2008, A fast randomized algorithm for overdetermined linear least-squares regression. Proceedings of the National Academy of Sciences, 105(36), pp 13212–13217.

[6] P.-G. Martinsson and J. A. Tropp, 2020, Randomized numerical linear algebra: Foundations and algorithms. Acta Numerica, 29, 403–572.

[7] R. S. Srinivasa, M. A. Davenport and J. Romberg, 2019, Trading Beams for Bandwidth: Imaging with Randomized Beamforming. SIAM J. Imag. Sci., vol. 13, no. 1, pp. 317-350.

Minimum entry qualification - an Honours degree at 2:1 or above (or International equivalent) in a relevant science or engineering discipline, possibly supported by an MSc Degree. 

This project requires a student with a high level of mathematics or numeracy.

Further information on English language requirements for EU/Overseas applicants.