Bayesian compressed sensing for nanoscale chemical mapping in the mid-infrared regime

• Applicants: Dr. Clemens Elster; Professor Dr. Eckart Rühl
• Subject Area: Physical Chemistry of Molecules, Liquids and Interfaces, Biophysical Chemistry ; Theoretical Condensed Matter Physics
• Term: from 2019 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 429434336

Functional nanomaterials provide the basis for novel forms of electronics, sensing or therapeutics. Their understanding and design requires fabrication informed by nanoscale chemical mapping. Novel scanning probe based spectroscopy using broadband infrared radiation emerged as a promising imaging technique at nanometer spatial resolution. However, the pixel-by-pixel data acquisition and conventional Fourier-transform schemes lead to prohibitive imaging times and enhanced radiation damage. This project aims to overcome this application barrier by developing a novel hyperspectral imaging scheme based on Bayesian compressed sensing (BCS). The project advances 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 will be 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 recent preliminary work. However, the number of required measurements is still too large. To further decrease the number of required measurements, a Bayesian variant of compressed sensing will be 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 proposed scheme will not only make hyperspectral imaging viable at the nanoscale, 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.

• DFG Programme: Research Grants
• Co-Investigator: Dr. Bernd Kästner