Andrew Thompson's homepage
Visiting Researcher, Mathematical Institute, University of Oxford
About me
I am a Senior Research Scientist at the National Physical Laboratory and a Visiting Researcher in the Mathematical Institute at the University of Oxford, and my research interests are in sparse estimation, compressed sensing and matrix completion, including applications to 5G wireless communications and image processing.

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Publications
  • A divide-and-conquer algorithm for binary matrix completion; To appear Linear Algebra and its Applications (2020) (with M. Beckerleg).
  • CHIRRUP: a practical algorithm for unsourced multiple access; Information and Inference (2019) (with R. Calderbank). Matlab code for the algorithm is here.
  • Sketching for Sequential Change-Point Detection; EURASIP Journal on Advances in Signal Processing 2019:42 (2019) (with Y. Cao, M. Wang and Y. Xie).
  • Matrix rigidity and the ill-posedness of Robust PCA and matrix completion; SIAM Journal on the Mathematics of Data Science 1(3) (2019) (with J. Tanner and S. Vary).
  • Sparse non-negative super-resolution --- simplified and stabilised; to appear Applied and Computational Harmonic Analysis (2019) (with A. Eftekhari, J. Tanner, B. Toader and H. Tyagi).
  • Sparse Inverse Problems Over Measures: Equivalence of the Conditional Gradient and Exchange Methods; SIAM Journal on Optimization 29(2) p1329-1349 (2019) (with A. Eftekhari).
  • The Cascading Haar Wavelet algorithm for computing the Walsh-Hadamard Transform; IEEE Signal Processing Letters 24(7) p1020-1023 (2017).
  • Dual-wavelength pump-probe microscopy analysis of melanin composition; Scientific Reports 6 (2016) (with F. Robles, J. Wilson, S. Deb, R. Calderbank and W. Warren).
  • Quantitative recovery conditions for tree-based compressed sensing; IEEE Transactions on Information Theory 63(3) p1-17 (2016) (with C. Cartis); extended technical report.
  • Data Representation using the Weyl Transform; IEEE Transactions on Signal Processing 64(7) p1844-1853 (2016) (with Q. Qiu, R. Calderbank and G. Sapiro).
  • Modified DCTNet for audio signals classification; The Journal of the Acoustical Society of America 140(4) (2016) (with Y. Xian, Y. Pu, Z. Gan and L. Liang).
  • On block coherence of frames; Applied and Computational Harmonic Analysis 38(1) p50-71 (2015) (with R. Calderbank and Y. Xie).
  • A new and improved quantitative recovery analysis for iterative hard thresholding algorithms in compressed sensing; IEEE Transactions on Information Theory 61(4) p1-24 (2015) (with C. Cartis).
  • An exact tree projection algorithm for wavelets; IEEE Signal Processing Letters 20(11) p1028-1031 (2013) (with C. Cartis). Matlab code for the algorithm is here.
  • Phase Transitions for Greedy Sparse Approximation Algorithms; Applied and Computational Harmonic Analysis 30(2) p188-203 (2011) (with J. Blanchard, C. Cartis and J. Tanner).
  • On Support Sizes of Restricted Isometry Constants; Applied and Computational Harmonic Analysis 29(3) p382-390 (2010) (with J. Blanchard).
  • Conference proceedings and preprints
  • Model-based algorithms for phenotyping from 3D imaging of dense wheat crops; IEEE International Workshop on Metrology for Agriculture and Forestry (2019) (with V. Livina, P. Harris, I. Mohamed and R. Dudley).
  • The dual approach to non-negative super-resolution: impact on primal reconstruction accuracy; Sampling Theory and Aplplications, Bordeaux, France (2019) (with S. Chretien and B. Toader).
  • Non-negative super-resolution is stable; IEEE Data Science Workshop, Lausanne, Switzerland (2018) (with A. Eftekhari, J. Tanner, B. Toader and H. Tyagi).
  • Compressed Neighbour Discovery using Sparse Kerdock Matrices; International Symposium on Information Theory, Vail, Colorado (2018) (with R. Calderbank).
  • Sparse near-equiangular tight frames with applications in full duplex wireless communication; Global Conference on Signal and Information Processing, Montreal, Canada (2017) (with R. Calderbank).
  • Compressive imaging using fast transform coding; Proceedings of the SPIE 9992, Emerging Imaging and Sensing Technologies, Edinburgh, UK (2016) (with R. Calderbank).
  • Sketching for Sequential Change-Point Detection; Global Conference on Signal and Information Processing, Orlando, USA (2015) (with Y. Xie and M. Wang).
  • Representation using the Weyl Transform; International Conference on Learning Representations, San Diego, USA (2015) (with Q. Qiu, R. Calderbank and G. Sapiro).
  • Classification of whale vocalizations using the Weyl Transform; International Conference on Acoustics, Speech and Signal Processing, Brisbane, Australia (2015) (with Y. Xian, Q. Qiu, L. Nolte, J. Lu, R. Calderbank and D. Nowacek).
  • Compressive Single-Pixel Imaging; IMA Conference on Mathematics in Defence, Defence Academy, Shrivenham, UK (2011).
  • Compressive Single-Pixel Imaging; Technical Report ERGO 11-006 (2011). This report relates to an internship carried out at SELEX Galileo Ltd, Edinburgh.
  • Pushing the RIP Phase Transition in Compressed Sensing; European Signal Processing Conference, Aalborg, Denmark (2010) (with J. Blanchard).
  • PhD thesis
  • Quantitative analysis of algorithms for compressed signal recovery; School of Mathematics, University of Edinburgh; supervisor: Coralia Cartis (2012).
  • Slides
  • Dual approaches to grid-free sparse inverse problems (IMA Conference on Numerical Linear Algebra and Optimization; Jun 2018).
  • Compressed Neighbour Discovery using Sparse Kerdock Matrices (International Symposium on Information Theory; Jun 2018).
  • The Cascading Haar Wavelet algorithm for computing the Walsh-Hadamard Transform (Global Conference on Signal and Information Processing; Nov 2017).
  • Sparse near-equiangular tight frames with applications in full duplex wireless communication (Global Conference on Signal and Information Processing; Nov 2017).
  • Patch Weyl Transform convolutional filters for learning image texture features (IMA Conference on the Mathematical Challenges of Big Data; Dec 2016).
  • Compressive imaging using fast transform coding (SPIE Security+Defence: Emerging Imaging and Sensing Technologies; Sep 2016).
  • Constructing matrices with optimal block coherence (SIAM Annual Meeting, Chicago, USA; Jul 2014).
  • A tree projection algorithm for wavelet-based sparse approximation (Biennial Conference on Numerical Analysis and Optimization, Strathclyde, UK; Jun 2013).
  • Compressive single-pixel imaging (IMA conference on Mathematics in Defence, Defence Academy, UK; Oct 2011).
  • A new recovery analysis of Iterative Hard Thresholding for compressed sensing (Signal Processing with Adaptive Sparse Structured Representations, Edinburgh, UK; Jun 2011).
  • On support sizes of restricted isometry constants (British Applied Mathematics Colloquium, Edinburgh, UK; Apr 2010).
  • Phase transitions for greedy sparse approximation algorithms (Curves and Surfaces, Avignon, France; Jun 2010).


  • Contact
    National Physical Laboratory
    Maxwell Centre
    Cavendish Laboratory
    J J Thomson Avenue
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