Noise Removal by Crystallographic Averaging and Information Content of an Image With Respect to Detections of Plane Symmetries

Published In

Proceedings of Microscopy & Microanalysis

Document Type

Citation

Publication Date

7-2016

Abstract

Crystallographic Image Processing (CIP) allows for the extraction of good estimates of the phases of the structure factors of many inorganic crystalline materials when the conditions of the (pseudo) weak phase object approximation are met in parallel-illumination high-resolution transmission electron microscopy (TEM) [1]. In atomic-resolution scanning TEM, CIP has been employed to remove noise from images and to confirm the average alkali-metal content per unit cell in a type I silicon clathrate [2]. The CIP technique has also been utilized to improve the signal to noise ratio (S/N) of scanning probe microscopy (SPM) images, reveal individual molecules more clearly [3,4], and remove the effects of multiple scanning probe mini-tips on a blunt scanning tunneling microscope (STM) tip from the images [5]. Because spatial averaging in CIP is done over all "asymmetric fraction" of all unit cells of regular 2D periodic arrays, this kind of noise removal from 2D periodic images is up to twelve times more effective [3,4] than traditional Fourier filtering [6].

The effectiveness of crystallographic averaging by CIP is demonstrated in Figure 1 on noisy images that were created with the popular freeware program GIMP on the basis of STM data that were published in ref. [7]. The first column of this figure shows the effect of traditional Fourier filtering (p1 enforcing) on images with from top to bottom progressively worsening S/Ns. The second and third columns show the effects of crystallographic averagings in Fourier space that take plane symmetries p2 ("extra averaging factor" of 2 gained) and p4 ("extra averaging factor" of 4 gained) into account. The program CRISP [1] was used for these purposes and also for the determination of the entries in the table to the right of Fig. 1.

The conclusion on the most probable* plane symmetry (p4) that underlies this STM data [7] was reached on the basis of the application of our geometric Akaike information criterion (G-AIC) to the detection of the underlying 2D translation lattice [4]. These kinds of criteria are only applicable when there are negligible systematic errors [8], which should be the case for experiments with well calibrated modern STMs and TEMs. Traditional plane symmetry deviation quantifiers for symmorphic 2D space groups are the residuals of the Fourier coefficient amplitude (Ares) and phase (φres) [1,3,4] as listed in the table to the right of Fig. 1 for the (not shown) test images that underlie this demonstration. Note the increase of the difference between the phase residuals for p2 and p4 with reduced S/Ns. The square root of the ratio of two G-AIC values (that were calculated on the basis of squared plane symmetry deviation quantifiers) can be utilized as a measure of the noise dependent information content [8] of a STM, SPM, TEM, or scanning TEM image with respect to the detection of the underlying plane symmetry of the regular periodic array from which it was recorded [9].

The raw STM image [7] that served as foundation of Fig. 1 was run through a low-pass (Gaussian blur) filter before Gaussian noise was added in a systematic way. The insets in each row are histograms of the (not shown) gray-level test images that resulted from this addition of Gaussian noise to the same (not shown filtered) STM image. The table gives traditional plane symmetry deviation quantifiers [1,3,4] for these (not shown) images for selected plane symmetry groups and the average of all subgroups of p4mm other that p4 and p2. It is clear from the histograms and the table that the S/N gets progressively worse from top to bottom.

Description

Published abstract © Microscopy Society of America 2016.

DOI

10.1017/S1431927616003664

Persistent Identifier

https://archives.pdx.edu/ds/psu/25904

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