Applications of Infinite Dimensional Compressive Sensing to Multi-Dimensional Analog Images using Machine Learning to Enhance Results

Working with SenseAI, the objective of this project is to develop a STEM imaging system based on infinite-dimensional CS that optimises a sampling strategy involving a continuous probe position domain as opposed to the current finite methods where the locations of the probes are a priori fixed while the recovery algorithm maps subsampled data to an analog image with low computational complexity. Such a capability would significantly increase the key metrics of resolution, precision and sensitivity, providing an increased capability for STEM to deliver unique scientific results. As many scientific methods generate images in similar manners, this approach will have a wide impact.
STEM imaging consists of a focused electron beam (or probe) scanning over a thin sample, while a range of different scattering signals are simultaneously collected (creating a time resolved hyperspectral dataset). Low-dose and fast STEM imaging is now a reality thanks to the application of Compressive Sensing (CS) to all imaging modes in the microscope. Specifically, in STEM compressive sensing allows the instrument to sub-sample the probe positions at rates dramatically lower than the Shannon-Nyquist sampling rate, provided that the target image has a sparse representation in a dictionary or basis, e.g., Discrete Cosine Transform. However, while this methodology has been shown to work, the existing CS STEM frameworks are based on finite-dimensional CS: they concern the recovery of a discrete (or pixelated) image. The issue limiting the power of these reconstructions to generate scientific insights at the moment is that STEM images are in fact analog (or continuous-space) and the application of finite-dimensional CS can lead to artefacts in the reconstruction that, in some cases, makes it difficult to distinguish the real features. The images may also in some cases not be sparse in a basis but possess an asymptotic sparsity, and therefore, the experimental sampling strategy of probe positions needs be to take account of these two factors.
Initial applications of this technology have focused on electron microscopy, where a real time acquisition mode for atomic resolution images/spectroscopy has been developed in which inpainting reconstructions are aided by a critical deep learning step - the microscopes are learning how to take the best images for themselves and then optimising the experimental acquisition. SenseAI is now working with several major instrument manufacturers to broaden these new approaches to instruments using X-rays, ions, neutrons and optics in addition to the existing portfolio of electron microscopes, with the goal of developing self-driving acquisition and analysis capabilities in the near future.