Microscopy is a pillar of modern science, which enables us to understand, inspect and improve on nature. While the technology of modern microscopes has progressed by leaps and bounds in the past decades, the methods used by microscopists to analyze data remain primitive. Common to new and emerging modalities of microscopy is the generation of massive, multi-dimensional data sets. This project develops fundamental analysis tools to extract basic motifs from these datasets; in particular, from data produced by scanning tunneling microscopes. These analysis tools will transform microscopy imaging by improving the quality and statistical significance of atomic-scale observations of materials. Key analysis goals that will be addressed include guarantees that algorithms produce models which accurately reflect the physics of the material of interest, and that algorithms perform reliably on practical data which may contain noise and errors. Key experimental goals include the generation of large scale data sets from multiple microscopy modalities which will be used to test and extend the analysis tools.
The project leverages recent advances in high-dimensional nonconvex optimization to address fundamental challenges in convolutional data modeling, the problem of modeling data as superpositions of translated motifs. Because the goal is to produce accurate information about novel materials whose properties are not yet understood, the investigators seek algorithms which exhibit (i) guaranteed performance,(ii) robustness to gross errors and (iii) scalability to massive, high-dimensional datasets. Building on recent progress in dictionary learning, the investigators study the properties of efficient methods for recovering models with one or more motifs. They seek highly scalable algorithms for these problems, using Riemannian optimization and active set methods. They study variants which are robust to commonly occurring gross errors, including pixel and scanline corruption, and contrast variations. The algorithms are applied to study materials for which previous analysis methodologies fail, including materials with multiple types of defects, quasiparticle interference, and high temperature superconductors. For each of these materials, high resolution scanning tunneling microscopy and spectroscopic imaging will be performed to produce large-scale, multidimensional data sets. Data sets on well-studied materials will be used to test and verify analysis algorithms, and the application of these algorithms to data sets on novel materials will be used to transform our understanding of the electronic structure of complex materials. Data sets on other microscopy modalities will also be obtained to generalize analysis tools to multiple scales in space, time and energy.
