Dr Anders Hansen

Anders

Anders leads the Applied Functional and Harmonic Analysis group within the Cambridge Centre for Analysis at DAMTP. He is a Lecturer at DAMTP, a Royal Society University Research Fellow and also a Fellow of Peterhouse College.

Tel: +44 1223 760403
Email: ach70 [at] cam.ac.uk

Resume

Teaching

Part III course on Compressed Sensing (2014). For last year's course and slides, click here.

Research interests

Functional Analysis (applied), Operator/Spectral theory, Compressed Sensing, Mathematical Signal Processing, Sampling Theory, Computational Harmonic Analysis, Inverse Problems, Complexity Theory, Geometric Integration, Numerical Analysis, C*-algebras

Papers

  1. J. Ben-Artzi, A. C. Hansen, O. Nevanlinna, M. Seidel, Can everything be computed? - On the Solvability Complexity Index and Towers of Algorithms.
  2. B. Adcock, A. C. Hansen, B. Roman, A note on compressed sensing of structured sparse wavelet coefficients from subsampled Fourier measurements.
  3. B. Adcock, A. C. Hansen, G. Kutyniok, J. Ma, Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements.
  4. B. Adcock, A. C. Hansen, C. Poon, B. Roman, Breaking the coherence barrier: A new theory for compressed sensing.
  5. A. Jones, B. Adcock, A. C. Hansen, , On asymptotic incoherence and its implications for compressed sensing for inverse problems.
  6. B. Adcock, A. C. Hansen, E. Herrholz, G. Teschke, Generalized sampling, infinite-dimensional compressed sensing, and semi-random sampling for asymptotically incoherent dictionaries.
  7. B. Adcock, A. C. Hansen, Generalized Sampling and Infinite Dimensional Compressed Sensing.
  8. A. C. Hansen, B. Roman, C. Wong, On the computation of spectra and pseudo spectra of self-adjoint and non-self-adjoint operators.
  9. A. C. Hansen, The infinite dimensional QR-algorithm.
  10. B. Adcock, A. C. Hansen, B. Roman, The quest for optimal sampling: computationally efficient, structure-exploiting measurements for compressed sensing, Compressed Sensing and its Applications, Springer (to appear)
  11. B. Adcock, M. Gataric, A. C. Hansen, On stable reconstructions from univariate nonuniform Fourier measurements, SIAM Jour. Imag. Scien.
  12. B. Adcock, A. C. Hansen, B. Roman, G. Teschke, Generalized sampling: stable reconstructions, inverse problems and compressed sensing over the continuum, Adv. in Imag. and Electr. Phys. 182, 187-279
  13. B. Adcock, A. C. Hansen, A. Shadrin, A stability barrier for reconstructions from Fourier samples SIAM Jour. on Num. Anal. 52, no. 1, 125-139
  14. B. Adcock, A. C. Hansen, C. Poon, B. Roman, Breaking the coherence barrier: asymptotic incoherence and asymptotic sparsity in compressed sensing, Proc. of the 10th Int. Conf. on Samp. Theory and Appl., 2013
  15. B. Adcock, A. C. Hansen, C. Poon, Optimal wavelet reconstructions from Fourier samples via generalized sampling, Proc. of the 10th Int. Conf. on Samp. Theory and Appl., 2013
  16. B. Adcock, A. C. Hansen, C. Poon, Beyond Consistent Reconstructions: Optimality and Sharp Bounds for Generalized Sampling, and Application to the Uniform Resampling Problem SIAM Jour. on Math. Anal. 45, no. 5, 3132-3167
  17. B. Adcock, A. C. Hansen, C. Poon, On optimal wavelet reconstructions from Fourier samples: linearity and universality of the stable sampling rate Appl. Comput. Harmon. Anal. (to appear)
  18. B. Adcock, A. C. Hansen, Generalized sampling and the stable and accurate reconstruction of piecewise analytic functions from their Fourier coefficients, Math. Comp. (to appear)
  19. B. Adcock, A. C. Hansen, E. Herrholz, G. Teschke, Generalized Sampling: Extensions to Frames and Inverse and Ill-Posed Problems, Inverse Prob. 29, no. 1, 015008
  20. B. Adcock, A. C. Hansen, Reduced Consistency Sampling in Hilbert Spaces, Proc. of the 9th Int. Conf. on Samp. Theory and Appl., 2011
  21. A. C. Hansen, O. Nevanlinna, Complexity Issues in Computing Spectra, Pseudospectra and Resolvents, Banach Center Publ. (to appear)
  22. 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
  23. B. Adcock, A. C. Hansen, A Generalized Sampling Theorem for Stable Reconstructions in Arbitrary Bases, J. Fourier Anal. Appl. 18, no. 4, 685-716
  24. A. C. Hansen, A theoretical framework for backward error analysis on manifolds, J. Geom. Mech. 3, no. 1, 81 - 111
  25. 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
  26. A. C. Hansen, J. Strain, On the order of deferred correction, Appl. Numer. Math. 61, no. 8, 961-973
  27. A. C. Hansen, Infinite dimensional numerical linear algebra; theory and applications, Proc. R. Soc. Lond. Ser. A. 466, no. 2124, 3539-3559
  28. A. C. Hansen, On the approximation of spectra of linear operators on Hilbert spaces, J. Funct. Anal. 254, no. 8, 2092--2126
  29. A. C. Hansen, J. Strain, Convergence theory for spectral deferred correction, Preprint, UC Berkeley

Thesis

A. C. Hansen, On the approximation of spectra of linear Hilbert space operators, PhD Thesis.

Awards

  1. Smith-Knight/Rayleigh-Knight Prize 2007, On the approximation of spectra and pseudospectra of linear operators on Hilbert spaces
  2. John Butcher Award 2007 (joint with T. Schmelzer (Oxford)), A theoretical framework for backward error analysis on manifolds.