Career
- 2013-date: University Lecturer, DAMTP, University of Cambridge, UK
- 2012-date: Royal Society University Research Fellow, University of Cambridge, UKĀ
- 2012: Marie Curie Fellow, University of Vienna Austria
- 2009 -2012: Junior Research Fellow, University of Cambridge, Homerton College UK
- 2008 -2009: Von Karman Instructor, California Institute of Technology, USA
Research
Anders is a member of the Department of Applied Mathematics and Theoretical Physics and head of the Applied Functional and Harmonic Analysis research group. His current research interests include but are not limited to Functional Analysis (applied), operator/ Spectral Theory, Compressed Sensing, Mathematical Signal Processing, Sampling Theory, Compressed Sensing, Mathematical Signal Processing, Sampling Theory, Computational Harmonic Analysis, Inverse problems, Medical Imaging, Geometric Intergration, Numerical Analysis, C*- algebras.
Selected Publications
- A. C. Hansen, On the Solvability Complexity Index, the n-Pseudospectrum and Approximations of Spectra of Operators, J. Amer. Math. Soc. 24, no. 1, 81-124
- A. C. Hansen, On the approximation of Spectra of linear operators on Hilbert spaces, J. Funct. Anal. 254 no.8, 2092--2126
- A. C. Hansen, Infinite dimensional numerical linear algebra; theory and applications, Proc. R. Soc. Lond. Ser. A. 466, no.2124, 3539-3559
- B. Adcock, A. C. Hansen, Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon, Appl. Comput. Harmon. Anal. 32, no.3, 357-388
Publications
On instabilities of deep learning in image reconstruction and the potential costs of AI.
– Proc Natl Acad Sci U S A
(2020)
201907377
(DOI: 10.1073/pnas.1907377117)
Compressed sensing MRI with variable density averaging (CS-VDA) outperforms full sampling at low SNR.
– Physics in medicine and biology
(2020)
65,
045004
(DOI: 10.1088/1361-6560/ab63b7)
On the infinite-dimensional QR algorithm
– Numerische Mathematik
(2019)
143,
1
(DOI: 10.1007/s00211-019-01047-5)
How to Compute Spectra with Error Control
– Phys Rev Lett
(2019)
122,
250201
On the Stable Sampling rate for binary measurements and wavelet reconstruction
– Applied and Computational Harmonic Analysis
(2020)
48,
630
(DOI: 10.1016/j.acha.2018.08.004)
Density Theorems for Nonuniform Sampling of Bandlimited Functions Using Derivatives or Bunched Measurements
– Journal of Fourier Analysis and Applications
(2017)
23,
1311
(DOI: 10.1007/s00041-016-9504-8)
From Global to Local: Getting More from Compressed Sensing.
– SIAM News
(2017)
Sampling from binary measurements - on reconstructions from Walsh coefficients
– IEEE Xplore
(2017)
256
(DOI: 10.1109/sampta.2017.8024449)
Weighted frames of exponentials and stable recovery of multidimensional functions from nonuniform Fourier samples
– Applied and Computational Harmonic Analysis
(2017)
42,
508
(DOI: 10.1016/j.acha.2015.09.006)
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