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DFG Project 2020-2023: Bayesian compressed sensing for nanoscale chemical mapping in the mid-infrared regime


Spatial cluster analysis of Leishmania parasites - full dataset vs. reconstruction from 10% of data (left). Single spectral reconstruction and indication of reduced measurements (right).

The project advanced both, the mathematical concept of BCS as well as the scanning probe microscope (SPM) required for the implementation, with variable sample and interferometer positioning, and thus overcoming the conventional pixel-by-pixel SPM paradigm. A set of well-adapted samples, instrumental developments, and validation experiments was used to reach this goal. Compressed sensing is a well-established signal processing technique that enables the complete reconstruction of a continuous signal based on only a small number of measurements, provided that the signal has a sparse representation with respect to some basis. In scanning probe-based spectroscopy using broadband infrared radiation the spectra can be assumed to be sparse in a Fourier basis, and compressed sensing has already been applied successfully in this context in our previous work. However, the number of required measurements was still too large. To further decrease the number of required measurements, a Bayesian variant of compressed sensing was developed in this project that uses additional prior knowledge about the spectra. The additional prior knowledge consists of chemical fingerprints of the spectra obtained from previous measurements. In addition, the spectra are known to be smooth with respect to their spatial position. The inferred coefficients of the chemical fingerprints of the spectra constitute one particularly relevant result. Bayesian methods are well suited to account for the prior knowledge described above. Furthermore, they allow for a complete quantitative characterization of the coefficients of the chemical fingerprints through their marginal posterior probability distributions after integrating out all other nuisance parameters. The developed scheme will not only make hyperspectral imaging viable at the nanoscale, but it also promises major advancement for the discrimination capability and detection sensitivity in nanoscale chemical mapping in general. The resulting rapid chemical nano-imaging technique promises widespread use in academic and industrial settings for fundamental and applied nano- and biomaterials research.

Further information can be found here.



C. Elster, FB 8.4, Clemens.Elster(at)ptb.de

B. Kästner, FB 7.1, Bernd.Kaestner(at)ptb.de