## Research Areas

#### We develop new tools for multidimensional spectroscopy by puting into practice the recent achievements of applied mathemathics. Among them, the area of compressed sensing (CS) particularly attracts our attention.

The key idea of CS is a new signal sampling theorem [1] stating, that in many cases the perfect reconstruction of a signal can be achieved with much smaller number of samples than assumed by a conventional sampling theory [2]. The group of methods is developing very rapidly and found applications in many fields of science, e.g. MRI [3], astronomy [4], biology [5] and many others. It was also introduced to NMR spectroscopy [6]. In case of NMR, the use of CS allows the significant shortening of experiments and the implementation of novel techniques that are infeasible with conventional sampling.

Currently, our group works on the theory and practice of CS-NMR by developing new signal processing algorithms and signal acquisition methods. We elaborate techniques dedicated for particular cases of NMR experiments – analysis of chemical reactions and processes [7], NMR diffusometry [8,9] and relaxometry and metabolomics.

The laboratory provides an access to equipment for NMR of proteins, solid state materials and suspensions. We are open to the scientific collaboration with academic and industrial groups.

### References

- Candes E, Romberg J, Tao T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE T. Inform. Theory 2006, 52:489–509
- Nyquist H. Certain topics in telegraph transmission theory. Transactions of the American Institute of Electrical Engineers, 1928, 47(2):617–644

Lustig M., Donoho D., Pauly J.M.. Sparse MRI: The application of compressed sensing for rapid MR imaging. Magnetic Resonance in Medicine 2007, 58(6):1182–1195 - Scaife A.M.M., Wiaux. Y. The application of compressed sensing techniques in radio astronomy.In 2011 30th URSI General Assembly and Scientific Symposium 2011, URSIGASS 2011
- Erlich Y.,Gordon A., Brand M., Hannon G.J., Mitra P.P.. Compressed genotyping. IEEE Transactions on Information Theory 2010, 56(2):706–723
- Kazimierczuk K., Orekhov V.Yu. Accelerated NMR spectroscopy by using compressed sensing 2011, Angew. Chem. Int. Ed. Engl., 50(24):5556–9
- Bermel W, Dass R, Neidig K-P, Kazimierczuk K. Two-dimensional NMR spectroscopy with temperature-sweep, ChemPhysChem 2014, 15: 1-4
- Urbańczyk M, Bernin D, Koźmiński W, Kazimierczuk K. Iterative Thresholding Algorithm for Multiexponential Decay Applied to PGSE NMR Data, Anal Chem 2013, 85 (3), 1828-1833
- Urbańczyk M, Koźmiński W, Kazimierczuk K. Accelerating diffusion-ordered NMR spectroscopy by joint sparse sampling of diffusion and time dimensions, Angew Chem Int Edit, 2014, 126: 1-5