Computation of 2-D spectra assisted by compressed sampling

The computation of scientific data can be very time consuming even if they are ultimately determined by a small number of parameters. The principle of compressed sampling suggests that we can achieve a considerable decrease in the computation time by avoiding the need to sample the full data set. We demonstrate the usefulness of this approach at the hand of 2-D spectra in the context of ultra-fast non-linear spectroscopy of biological systems where numerical calculations are highly challenging due to the considerable computational effort involved in obtaining individual data points.

[1]  Emmanuel J. Candès,et al.  Matrix Completion With Noise , 2009, Proceedings of the IEEE.

[2]  Justin R. Caram,et al.  Dynamics of electronic dephasing in the Fenna–Matthews–Olson complex , 2010 .

[3]  David Gross,et al.  Recovering Low-Rank Matrices From Few Coefficients in Any Basis , 2009, IEEE Transactions on Information Theory.

[4]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[5]  X. Andrade,et al.  Application of compressed sensing to the simulation of atomic systems , 2012, Proceedings of the National Academy of Sciences.

[6]  C. Kreisbeck,et al.  Modelling of oscillations in two-dimensional echo-spectra of the Fenna–Matthews–Olson complex , 2011, 1110.1511.

[7]  Emmanuel J. Candès,et al.  Exact Matrix Completion via Convex Optimization , 2009, Found. Comput. Math..

[8]  Semion K. Saikin,et al.  Probing Biological Light-Harvesting Phenomena by Optical Cavities , 2011, 1110.1386.

[9]  D. Gross,et al.  Efficient quantum state tomography. , 2010, Nature communications.

[10]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[11]  Emmanuel J. Candès,et al.  A Singular Value Thresholding Algorithm for Matrix Completion , 2008, SIAM J. Optim..

[12]  S. Huelga,et al.  The nature of the low energy band of the Fenna-Matthews-Olson complex: vibronic signatures. , 2011, The Journal of chemical physics.

[13]  M. Cho.  Two-Dimensional Optical Spectroscopy , 2009 .

[14]  G. Fleming,et al.  Unified treatment of quantum coherent and incoherent hopping dynamics in electronic energy transfer: reduced hierarchy equation approach. , 2009, The Journal of chemical physics.

[15]  S. Mukamel.  Principles of Nonlinear Optical Spectroscopy , 1995 .

[16]  T. Mančal,et al.  Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems , 2007, Nature.

[17]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[18]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[19]  C. Kreisbeck,et al.  Long-Lived Electronic Coherence in Dissipative Exciton Dynamics of Light-Harvesting Complexes , 2012, 1203.1485.

[20]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[21]  Justin R Caram,et al.  Long-lived quantum coherence in photosynthetic complexes at physiological temperature , 2010, Proceedings of the National Academy of Sciences.

[22]  Shiqian Ma,et al.  Fixed point and Bregman iterative methods for matrix rank minimization , 2009, Math. Program..

[23]  Martin B. Plenio,et al.  Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials , 2010, 1006.4507.

[24]  Javier Prior,et al.  Efficient simulation of strong system-environment interactions. , 2010, Physical review letters.

[25]  D. Tronrud,et al.  The structural basis for the difference in absorbance spectra for the FMO antenna protein from various green sulfur bacteria , 2009, Photosynthesis Research.

[26]  Emmanuel J. Candès,et al.  NESTA: A Fast and Accurate First-Order Method for Sparse Recovery , 2009, SIAM J. Imaging Sci..