Compressed sensing for STEM tomography

Abstract

A central challenge in scanning transmission electron microscopy (STEM) is to reduce the electron radiation dosage required for accurate imaging of 3D biological nano-structures. Methods that permit tomographic reconstruction from a reduced number of STEM acquisitions without introducing significant degradation in the final volume are thus of particular importance. In random-beam STEM (RB-STEM), the projection measurements are acquired by randomly scanning a subset of pixels at every tilt view. In this work, we present a tailored RB-STEM acquisition-reconstruction framework that fully exploits the compressed sensing principles. We first demonstrate that RB-STEM acquisition fulfills the "incoherence" condition when the image is expressed in terms of wavelets. We then propose a regularized tomographic reconstruction framework to recover volumes from RB-STEM measurements. We demonstrate through simulations on synthetic and real projection measurements that the proposed framework reconstructs high-quality volumes from strongly downsampled RB-STEM data and outperforms existing techniques at doing so. This application of compressed sensing principles to STEM paves the way for a practical implementation of RB-STEM and opens new perspectives for high-quality reconstructions in STEM tomography.

Experimental Evaluation of Undersampling Schemes for Electron Tomography of Nanoparticles

“…Hence, for a fixed electron dose, it is preferential to spread the total amount of electrons across as many pixels as possible. Earlier theoretical predictions on the capacity of R‐US to outperform T‐US, are not in agreement with the experimental findings in this work. For a similar angular range and increment, no large difference between R‐US and T‐US was detected.…”

“…Donati et al used simulated R‐US projection images to show that the incorporated approach, defined by Equation , leads to more accurate reconstructions in comparison to previous work wherein the R‐US projection data were first restored by CS and afterward used as input for reconstruction . Here, we will verify these findings based on experimental data.…”

“…Lustig et al used transform point spread function (TPSF) analysis within the context of CS‐MRI to demonstrate that radial sampling of the object's Fourier space results into sufficient incoherence to apply CS . This analysis was extended toward electron tomography for a specific type of I‐US for which subsets of pixels are measured in a random manner . In this study it was validated that measuring randomly selected pixels is sufficiently incoherent to the Haar wavelet, and therefore discrete gradient domain, to fulfill the incoherence criterion.…”

“…Recently, the idea of performing tomographic reconstructions of R‐US tilt series by exploiting the principles of CS was theoretically demonstrated. The superiority of R‐US over T‐US approaches for electron tomography reconstructions was displayed, albeit using simulated data . On the other hand, Van den Broek et al evidenced that when using the same dose, CS restoration of 2D R‐US images does not outperform denoising I‐US images under counting noise conditions .…”

In situstructural analysis of the flagellum attachment zone inTrypanosoma bruceiusing cryo-scanning transmission electron tomography

“…Several strategies based on sparse acquisition exist to efficiently reduce the electron dose 455 in STET but have only been applied to non-cryo samples (Trépout, 2019;Vanrompay et al, 2019). By 456 combining such sparse data collection schemes and dedicated algorithm to reconstruct sparse data 457 (Donati et al, 2017;Leary et al, 2013), greater magnifications would be allowed, thus improving the 458 resolution currently available in cryo-STET. 459…”