Non‐local averaging in
EM
: decreasing the required electron dose in crystal image reconstruction without losing spatial resolution
Authors: Mevenkamp Niklas , Berkels Benjamin 
Published: December 2016

Todays electron microscopes enable imaging of materials at atomic resolution. However, in many relevant applications, the resolution is not limited by the microscope's physical properties, but by the beam sensitivity of the material. The beam sensitivity limits the applicable electron dose before beam damage corrupts the measurement, which leads to low signal‐to‐noise ratios (SNR). The SNR in turn limits the effective resolution, or, in other words, the precision of any analysis performed on the measurement.

Typically, the SNR is improved either by local averaging or by averaging multiple aligned images of the same specimen. Unfortunately, the former reduces the effective spatial resolution of the image, while the latter increases the applied electron dose. We propose to circumvent these issues by combining the benefits of both approaches in a single method. The key observation is that most EM measurements (e.g. (S)TEM, EELS, EDX) of atomic resolution contain many self‐similar regions: due to the crystal structure, any unit cell is typically pictured more than once. This is an ideal setting for non‐local averaging methods, which have become very popular over the past few years due to their ability of substantially reducing noise without blurring the image.

The gold standard amongst modern non‐local averaging algorithms in general digital photography is the Block‐matching and 3D filtering algorithm (BM3D) [1]. However, due to its generality, BM3D does not make full use of the aforementioned rich self‐similarity typically found in atomic scale micrographs. Thus, we propose a denoising strategy based on BM3D, but specially tailored to atomic scale electron micrographs [2]. The key feature is a new method for the automated analysis of the projected specimen geometry from the image, i.e. the detection of regions with different crystal structure [3] as well as their primitive unit cell dimensions [4]. This information allows us to predict the position of similar image parts, thus maximizing the potential of BM3D.

Most single image averaging techniques, including BM3D, are designed to remove Gaussian noise. However, aside from approximately Gaussian noise generated by the sensor itself, EM measurements typically contain contributions of Poisson noise as well due to the electron counting statistics. To address this issue, we developed an automated procedure for estimating the parameters of a mixed Poisson‐Gaussian noise model directly from raw EM data, which allows the use of averaging techniques designed for Gaussian noise removal.

Compared to the commonly used local averaging techniques, our proposed method achieves significantly higher effective resolution. Furthermore, our method can be easily combined with the aforementioned alignment and averaging techniques for multiple images of the same specimen, thus significantly reducing the electron dose required for a useful reconstruction.

Figure 1 demonstrates the proposed method on an exemplary HAADF‐STEM image with three crystal regions (SrTiO
3
, BaTiO
3
and SrRuO
3
) [5]. Figure 1a shows the electron micrograph and indicates the detected region boundaries (green), as well as the lattice vectors of a primitive unit cell within each of the three crystals (red). The result of non‐local averaging with the proposed method is shown in Figure 1b. A zoom into a region around the bottom crystal inferface is given (yellow) that simplifies the assessment of the increase in SNR. While in the original STEM image, the distinction between the SrTiO
3
and BaTiO
3
regions is hardly possible with the naked eye, the increased contrast of the denoised image makes it clearly visible.

In Figure 2a we show a few selected spectra of an EELS dataset with a low SNR especially in the last components of the spectrum [6]. Figure 2b shows the corresponding spectra after denoising with the proposed method. The result demonstrates that the proposed method also applies very well to hyper‐spectral data and excels at significantly increasing the SNR of the spectra without introducing artifacts or blurring fine details.