A Hybrid Frequency-Spatial Domain Model For Sparse Image Reconstruction In Scanning Transmission Electron Microscopy

Scanning transmission electron microscopy(STEM)is a powerful and widely used technique in high-resolution atomic imaging of materials,which achieves high spatial resolution better than 0.5 (?).However,an order of magnitude for electron beam doses(typically in excess of 105-106 e-/(?)2)is necessary,in which the high-energy electron beam may burn the materials and destroy the original structures.Meanwhile,STEM utilizes high energy electron doses to scan material samples point by point,consuming lots of time and resources.Exploring how to image samples faster and how to extend the application range of STEM,the key point is how to obtain images with acceptable quality in decreased electron doses.Partially sampling with fixed electron doses and restoring the unsampled information by computational methods is one of the most important and widely used solutions.Traditional reconstruction methods in sparse sampling develop from basic frequency filter to compressed sensing framework.Frequency filter methods are only applicable for materials with a large range of fixed texture structures,and they can’t accurately determine the material boundaries,let alone any discrepancy between the internal structures.Optimizedbased compressed sensing methods execute fast,but have low reconstruction accuracy and work not good in electron microscopy images with low signal-noise-ratio.Bayesian-based compressed sensing methods adopt dictionary learning strategy and have high reconstruction accuracy,which can restore the complete structure in cases higher than 25%sample ratio.However,they need to calculate "endless" iterations,cannot meet the requirements of real-time imaging.With the rapid development of deep learning,people explore convolution neural network based reconstruction methods,which replace lots of iterations with one forward propagation,making the real-time imaging of low-dose STEM possible.These methods mainly inpaint the missing information by exploring the texture features from local patches.However,without strict theoretical guarantee,CS-based deep learning methods perform not well on inpainting problem in extremely sparse sampling cases,especially for real-world data with Poisson noise.Meanwhile,most networks adopt blockbased linear mapping as initial reconstruction,which significantly limits receptive field and loses the ability of global information extraction.Here,we propose a novel Frequency-Spatial Hybrid Network(FSHNet)to restore STEM images at an extremely low sampling rate,for example,atomic-scale STEM imaging with a sampling rate lower than 5%,which is impossible to be achieved by traditional methods.In FSHNet,the frequency domain information is filtered to ensure global similarity,and the detailed spatial domain information is captured with convolution operators to polish the local structure.By combining the global structure features from frequency filter and the local pixel information from convolution operators,FSHNet can achieve a complete structure restoration with clearer local details.Comprehensive experiments on the synthetic and real-world datasets show that our method gains 30%～50%performance enhancement,while retaining the real-time execution condition.