Quantifying the Advantages of Compressive Sensing and Sparse Reconstruction for Scanning Transmission Electron Microscopy

From the perspective of information theory, it's easy to suspect that current methods for extracting information using STEM can't possibly be optimal. After all, when we try to make sense of the multiGB data sets produced by spectrum imaging, STEM diffraction, and other similar techniques, usually the first thing we do is apply aggressive data reduction techniques. Each EELS spectrum might be represented as a combination of a small number of component spectra (using any of a variety of techniques including principal component analysis, independent component analysis, and Bayesian dictionary learning), and the residual is normally thrown away as noise. In STEM diffraction, often an entire diffraction pattern with a MB or more of data is reduced to just three parameters giving the 3D orientation of the crystal at that point. In both cases, the analyzed data might be 100 times smaller than the raw data and yet may still contain virtually all of the information the user cared about.