# Dr Anders Hansen

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

## 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

- J. Ben-Artzi, A. C. Hansen, O. Nevanlinna, M. Seidel,
*Can everything be computed? - On the Solvability Complexity Index and Towers of Algorithms*. - B. Adcock, A. C. Hansen, B. Roman,
*A note on compressed sensing of structured sparse wavelet coefficients from subsampled Fourier measurements*. - B. Adcock, A. C. Hansen, G. Kutyniok, J. Ma,
*Linear Stable Sampling Rate: Optimality of 2D Wavelet Reconstructions from Fourier Measurements*. - B. Adcock, A. C. Hansen, C. Poon, B. Roman,
*Breaking the coherence barrier: A new theory for compressed sensing*. - A. Jones, B. Adcock, A. C. Hansen, ,
*On asymptotic incoherence and its implications for compressed sensing for inverse problems*. - B. Adcock, A. C. Hansen, E. Herrholz, G. Teschke,
*Generalized sampling, infinite-dimensional compressed sensing, and semi-random sampling for asymptotically incoherent dictionaries*. - B. Adcock, A. C. Hansen,
*Generalized Sampling and Infinite Dimensional Compressed Sensing*. - A. C. Hansen, B. Roman, C. Wong,
*On the computation of spectra and pseudo spectra of self-adjoint and non-self-adjoint operators*. - A. C. Hansen,
*The infinite dimensional QR-algorithm*. - 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) - B. Adcock, M. Gataric, A. C. Hansen,
*On stable reconstructions from univariate nonuniform Fourier measurements*, SIAM Jour. Imag. Scien. - 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 - 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*

- 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* - 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* - 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* - 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)* - 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)* - 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 - B. Adcock, A. C. Hansen,
*Reduced Consistency Sampling in Hilbert Spaces*,*Proc. of the 9th Int. Conf. on Samp. Theory and Appl., 2011* - A. C. Hansen, O. Nevanlinna,
*Complexity Issues in Computing Spectra, Pseudospectra and Resolvents*,*Banach Center Publ.*(to appear) - 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 - B. Adcock, A. C. Hansen,
*A Generalized Sampling Theorem for Stable Reconstructions in Arbitrary Bases*,*J. Fourier Anal. Appl.*18, no. 4, 685-716 - A. C. Hansen,
*A theoretical framework for backward error analysis on manifolds*,*J. Geom. Mech.*3, no. 1, 81 - 111 - 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, J. Strain,
*On the order of deferred correction*,*Appl. Numer. Math.*61, no. 8, 961-973 - A. C. Hansen,
*Infinite dimensional numerical linear algebra; theory and applications*,*Proc. R. Soc. Lond. Ser. A.*466, no. 2124, 3539-3559 - 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, 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

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