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

与SenseAI合作，该项目的目标是开发一种基于无限维CS的STEM成像系统，该系统优化了涉及连续探头位置域的采样策略，而不是目前的有限方法，其中探头的位置是先验固定的，而恢复算法将子采样数据映射到具有低计算复杂性的模拟图像。这种能力将显著提高分辨率、精度和灵敏度的关键指标，为STEM提供独特的科学成果提供更高的能力。由于许多科学方法都以类似的方式生成图像，因此这种方法将产生广泛的影响。STEM成像包括聚焦电子束（或探头）扫描薄样品，同时收集一系列不同的散射信号（创建时间分辨高光谱数据集）。由于压缩感知（CS）在显微镜中所有成像模式中的应用，低剂量和快速STEM成像现在成为现实。具体来说，在STEM压缩感知中，如果目标图像在字典或基中具有稀疏表示（例如，离散余弦变换），则允许仪器以显著低于香农-奈奎斯特采样率的速率对探头位置进行子采样。然而，虽然这种方法已被证明是有效的，但现有的CS STEM框架是基于有限维CS的：它们涉及到离散（或像素化）图像的恢复。目前，限制这些重建产生科学见解的能力的问题是，STEM图像实际上是模拟的（或连续空间的），有限维CS的应用可能导致重建中的伪影，在某些情况下，难以区分真实特征。在某些情况下，图像也可能在基上不是稀疏的，但具有渐近稀疏性，因此，探针位置的实验采样策略需要考虑这两个因素。这项技术的最初应用集中在电子显微镜上，其中已经开发了原子分辨率图像/光谱的实时采集模式，其中在绘画重建中借助于关键的深度学习步骤-显微镜正在学习如何为自己拍摄最佳图像，然后优化实验采集。SenseAI目前正与几家主要仪器制造商合作，在现有的电子显微镜产品组合之外，将这些新方法扩展到使用x射线、离子、中子和光学仪器的仪器，目标是在不久的将来开发自动驾驶采集和分析能力。

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.