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Bayes'sches Compressed Sensing zur chemischen Abbildung im Nanobereich unter Einsatz von Strahlung im mittleren Infrarotbereich

Fachliche Zuordnung Physikalische Chemie von Molekülen, Flüssigkeiten und Grenzflächen, Biophysikalische Chemie
Theoretische Physik der kondensierten Materie
Förderung Förderung von 2019 bis 2024
Projektkennung Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 429434336
 
Erstellungsjahr 2023

Zusammenfassung der Projektergebnisse

Imaging and characterization of molecular and electronic properties of matter is relevant to various fields of research. Combining scanning probe microscopy with infrared (IR) spectroscopy offers highresolution measurements beyond the classical diffraction limit. However, the pixel-by-pixel data acquisition used by this measurement technique leads to prohibitive imaging times and enhanced radiation damage. This project aimed to enhance the speed of scanning-based measurements and chemical detection sensitivity. To achieve this, advanced statistical methods, including compressed sensing, low-rank matrix recovery, and Bayesian inference were developed, which exceeded the scope of the proposal. We also improved scanning probe microscopy for variable sample and interferometer mirror positioning. Two low-rank matrix recovery methods have been developed based on hierarchical Bayesian modeling and conventional regularization. Both methods favor spatial smoothness through a Gaussian Markov random field prior and a corresponding regularization functional, respectively. Both methods reliably reconstructed complex biological sample data using only 5% randomly selected samples. The developed low-rank methods have been successfully applied to data from such different measurement techniques as nano-Fourier-transform IR (nano-FTIR) spectroscopy, focal plane array IR imaging, and atomic force microscopy-based IR spectroscopy (AFM-IR). A Python code implementation of the regularization method has been made publicly available. A joint regression and compressed sensing approach has been developed which allows for quantitative determination of the concentration of chemical components given chemical fingerprints from previous measurements and subsampled data only. A key feature of this compressive chemical mapping is that unknown additional sparse signal components are accounted for. Using randomly subsampled nano-FTIR data, it was demonstrated that this feature is crucial to arrive at a reliable quantification of the contained chemical components. The developed mathematical approaches save time by requiring only a small fraction of randomly selected pixels. However, the mechanical positioning underlying the scanning probe techniques would render such random sampling schemes inefficient due to idle routes and long positioning times. To address this, three realistic subsampling schemes based on continuous trajectories have been explored to eliminate idle routes and positioning delays. Using the developed low-rank matrix recovery procedure it was shown that all three considered subsampling schemes lead to results of a similar quality as random subsampling. Finally, these subsampling schemes have been implemented in a nano-FTIR setup to practically demonstrate the achieved advancements. Clear perspectives emerging from this successful project that has gone beyond the proposed aims have become evident from the experimental and mathematical point of view.

Projektbezogene Publikationen (Auswahl)

 
 

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