38 research outputs found
Consistent Basis Pursuit for Signal and Matrix Estimates in Quantized Compressed Sensing
This paper focuses on the estimation of low-complexity signals when they are
observed through uniformly quantized compressive observations. Among such
signals, we consider 1-D sparse vectors, low-rank matrices, or compressible
signals that are well approximated by one of these two models. In this context,
we prove the estimation efficiency of a variant of Basis Pursuit Denoise,
called Consistent Basis Pursuit (CoBP), enforcing consistency between the
observations and the re-observed estimate, while promoting its low-complexity
nature. We show that the reconstruction error of CoBP decays like
when all parameters but are fixed. Our proof is connected to recent bounds
on the proximity of vectors or matrices when (i) those belong to a set of small
intrinsic "dimension", as measured by the Gaussian mean width, and (ii) they
share the same quantized (dithered) random projections. By solving CoBP with a
proximal algorithm, we provide some extensive numerical observations that
confirm the theoretical bound as is increased, displaying even faster error
decay than predicted. The same phenomenon is observed in the special, yet
important case of 1-bit CS.Comment: Keywords: Quantized compressed sensing, quantization, consistency,
error decay, low-rank, sparsity. 10 pages, 3 figures. Note abbout this
version: title change, typo corrections, clarification of the context, adding
a comparison with BPD
SIM-STEM Lab: Incorporating Compressed Sensing Theory for Fast STEM Simulation
Recently it has been shown that precise dose control and an increase in the
overall acquisition speed of atomic resolution scanning transmission electron
microscope (STEM) images can be achieved by acquiring only a small fraction of
the pixels in the image experimentally and then reconstructing the full image
using an inpainting algorithm. In this paper, we apply the same inpainting
approach (a form of compressed sensing) to simulated, sub-sampled atomic
resolution STEM images. We find that it is possible to significantly sub-sample
the area that is simulated, the number of g-vectors contributing the image, and
the number of frozen phonon configurations contributing to the final image
while still producing an acceptable fit to a fully sampled simulation. Here we
discuss the parameters that we use and how the resulting simulations can be
quantifiably compared to the full simulations. As with any Compressed Sensing
methodology, care must be taken to ensure that isolated events are not excluded
from the process, but the observed increase in simulation speed provides
significant opportunities for real time simulations, image classification and
analytics to be performed as a supplement to experiments on a microscope to be
developed in the future.Comment: 20 pages (includes 3 supplementary pages), 15 figures (includes 5
supplementary figures), submitted to Ultramicroscop
SenseAI: Real-Time Inpainting for Electron Microscopy
Despite their proven success and broad applicability to Electron Microscopy
(EM) data, joint dictionary-learning and sparse-coding based inpainting
algorithms have so far remained impractical for real-time usage with an
Electron Microscope. For many EM applications, the reconstruction time for a
single frame is orders of magnitude longer than the data acquisition time,
making it impossible to perform exclusively subsampled acquisition. This
limitation has led to the development of SenseAI, a C++/CUDA library capable of
extremely efficient dictionary-based inpainting. SenseAI provides N-dimensional
dictionary learning, live reconstructions, dictionary transfer and
visualization, as well as real-time plotting of statistics, parameters, and
image quality metrics.Comment: Presented in ISCS2
High‐speed 4‐dimensional scanning transmission electron microscopy using compressive sensing techniques
Here we show that compressive sensing allows 4‐dimensional (4‐D) STEM data to be obtained and accurately reconstructed with both high‐speed and reduced electron fluence. The methodology needed to achieve these results compared to conventional 4‐D approaches requires only that a random subset of probe locations is acquired from the typical regular scanning grid, which immediately generates both higher speed and the lower fluence experimentally. We also consider downsampling of the detector, showing that oversampling is inherent within convergent beam electron diffraction (CBED) patterns and that detector downsampling does not reduce precision but allows faster experimental data acquisition. Analysis of an experimental atomic resolution yttrium silicide dataset shows that it is possible to recover over 25 dB peak signal‐to‐noise ratio in the recovered phase using 0.3% of the total data. Lay abstract: Four‐dimensional scanning transmission electron microscopy (4‐D STEM) is a powerful technique for characterizing complex nanoscale structures. In this method, a convergent beam electron diffraction pattern (CBED) is acquired at each probe location during the scan of the sample. This means that a 2‐dimensional signal is acquired at each 2‐D probe location, equating to a 4‐D dataset. Despite the recent development of fast direct electron detectors, some capable of 100kHz frame rates, the limiting factor for 4‐D STEM is acquisition times in the majority of cases, where cameras will typically operate on the order of 2kHz. This means that a raster scan containing 256^2 probe locations can take on the order of 30s, approximately 100‐1000 times longer than a conventional STEM imaging technique using monolithic radial detectors. As a result, 4‐D STEM acquisitions can be subject to adverse effects such as drift, beam damage, and sample contamination. Recent advances in computational imaging techniques for STEM have allowed for faster acquisition speeds by way of acquiring only a random subset of probe locations from the field of view. By doing this, the acquisition time is significantly reduced, in some cases by a factor of 10‐100 times. The acquired data is then processed to fill‐in or inpaint the missing data, taking advantage of the inherently low‐complex signals which can be linearly combined to recover the information. In this work, similar methods are demonstrated for the acquisition of 4‐D STEM data, where only a random subset of CBED patterns are acquired over the raster scan. We simulate the compressive sensing acquisition method for 4‐D STEM and present our findings for a variety of analysis techniques such as ptychography and differential phase contrast. Our results show that acquisition times can be significantly reduced on the order of 100‐300 times, therefore improving existing frame rates, as well as further reducing the electron fluence beyond just using a faster camera
Simultaneous High-Speed and Low-Dose 4-D STEM Using Compressive Sensing Techniques
Here we show that compressive sensing allow 4-dimensional (4-D) STEM data to
be obtained and accurately reconstructed with both high-speed and low fluence.
The methodology needed to achieve these results compared to conventional 4-D
approaches requires only that a random subset of probe locations is acquired
from the typical regular scanning grid, which immediately generates both higher
speed and the lower fluence experimentally. We also consider downsampling of
the detector, showing that oversampling is inherent within convergent beam
electron diffraction (CBED) patterns, and that detector downsampling does not
reduce precision but allows faster experimental data acquisition. Analysis of
an experimental atomic resolution yttrium silicide data-set shows that it is
possible to recover over 25dB peak signal-to-noise in the recovered phase using
0.3% of the total data