Typically, the Nyquist frequency determines the sampling rate required to resolve a specific feature in a dataset. In practice this requires oversampling by twice the maximum relevant frequency. As such this provides a lower limit for the electron dose necessary to acquire the data experimentally. However, by applying the compressive sensing (CS) principles of sparsity and incoherence, this limit can be overcome and therefore a substantial reduction of the total electron dose can be achieved. CS theory then allows a recovery of the essential image information from randomly undersampled images. The theory of CS has been successfully applied in a number of areas, e.g. astronomy, MRI scanning, electron tomography [1], and most recently first experimental designs for STEM have been reported [2,3]. Despite these developments, CS acquisition schemes able to recover quantifiable information from atomically resolved images of beam-sensitive materials, time-changing processes and spectroscopic datasets have so far not been established  for STEM.
Here we demonstrate such a CS-based STEM acquisition implementation and benchmark its performance at atomic resolution using a variety of materials, including complex oxide ceramics with an inhomogeneous distribution of point defects as illustrated in fig. 1, but also highly beam-sensitive catalysts with atomic resolution [4]. The implementation relies on custom-built hardware and software which controls an electrostatic beam shutter to blank the electron beam during all but a few randomly chosen pixels through a regular image (or indeed spectrum image) acquisition. The total electron dose used to form a whole dataset can thus be tailored according to the electron damage threshold of the sample under investigation whilst maintaining all other acquisition parameters identical to regular data acquisition, allowing a seamless transition from ‘fully sampled’ to ultra-low-dose conditions. It will be shown that datasets acquired in this fashion down to a few % of the total incoming dose (see fig. 2) can be reconstructed to yield a truthful atomic resolution representation of the sample, using a variety of reconstruction algorithms [5,6]. We show that this implementation of CS can also be extended to 2D spectroscopy mapping and simultaneous HAADF image acquisition.. These results open the door to practical ultra-low dose high-resolution imaging and spectroscopy in the STEM for very beam sensitive samples, where the level of sampling can simply be chosen depending on the damage threshold of the material being investigated [7].
References
[1] Z. Saghi et al., Nano Letters 11 (2011), 4666
[2] Q.M. Ramasse et al., 15th Frontiers of Electron Microscopy in Materials Sciences (FEMS); 2015, September 13-18; Tahoe City, California, p76;
[3] A. Béché et al. , Appl. Phys. Lett. 108 (2016)
[4] D. Mücke-Herzberg et al. submitted
[5] A. Stevens et al. , Microscopy 63 (2014), 41-5;
[6] J. Ma. et al. submitted
[7] SuperSTEM is the UK EPSRC National Facility for Aberration-Corrected STEM, supported by the Engineering and Physical Science Research Council. PNNL, a multiprogram national laboratory, is operated by Battelle for the U.S. Department of Energy under Contract No. DE-AC05-76RLO1830. PAM, ZS and RL acknowledge funding under ERC Advanced Grant 291522-3DIMAGE.

Figures:

Figure 1. Example CS shearlet reconstruction of NTCT (Ca stabilised Nd2/3 TiO3) at different values of undersampling showing correct identification of point defect [4].

Figure 2. Reduction of the normalized measured camera current with decrease of the % of exposed pixels per randomly untersampled image frame; the camera current exhibits excellent linearity with the % coverage, confirming that the total electron dose is effectively reduced by random undersampling. Data for three different blanking periods are shown, showing that the linearity in reduction of electron dose is consistently achieved.

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EMC Abstracts - http://emc-proceedings.com/abstract/a-compressive-sensing-based-acquisition-design-for-quantitative-ultra-low-dose-high-resolution-imaging-and-spectroscopy-in-the-stem/