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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

More chemical detection through less sampling: amplifying chemical signals in hyperspectral data cubes through compressive sensing

Compressive sensing (CS) is a method of sampling which permits some classes of signals to be reconstructed with high accuracy even when they were sampled at sub-Nyquist rates. In this paper we explore a phenomenon in which bandwise CS sampling of a hyperspectral data cube followed by reconstruction can actually result in amplification of chemical signals contained in the cube. Perhaps most surprisingly, chemical signal amplification generally seems to increase as the level of sampling decreases. In some examples, the chemical signal is significantly stronger in a data cube reconstructed from 10% CS sampling than it is in the raw, 100% sampled data cube. We explore this phenomenon in two real-world datasets including the Physical Sciences Inc. Fabry-Perot interferometer sensor multispectral dataset and the Johns Hopkins Applied Physics Lab FTIR-based longwave infrared sensor hyperspectral dataset. Each of these datasets contains the release of a chemical simulant, such as glacial acetic acid, triethyl phospate, and sulfur hexafluoride, and in all cases we use the adaptive coherence estimator (ACE) to detect a target signal in the hyperspectral data cube. We end the paper by suggesting some theoretical justifications for why chemical signals would be amplified in CS sampled and reconstructed hyperspectral data cubes and discuss some practical implications.

Hyperspectral imagery, Compressive Sensing, single↗
DOE OSTI2017

Acquisition of STEM Images by Adaptive Compressive Sensing

Compressive Sensing (CS) allows a signal to be sparsely measured first and accurately recovered later in software [1]. In scanning transmission electron microscopy (STEM), it is possible to compress an image spatially by reducing the number of measured pixels, which decreases electron dose and increases sensing speed [2,3,4]. The two requirements for CS to work are: (1) sparsity of basis coefficients and (2) incoherence of the sensing system and the representation system. However, when pixels are missing from the image, it is difficult to have an incoherent sensing matrix. Nevertheless, dictionary learning techniques such as Beta-Process Factor Analysis (BPFA) [5] are able to simultaneously discover a basis and the sparse coefficients in the case of missing pixels. On top of CS, we would like to apply active learning [6,7] to further reduce the proportion of pixels being measured, while maintaining image reconstruction quality. Suppose we initially sample 10% of random pixels. We wish to select the next 1% of pixels that are most useful in recovering the image. Now, we have 11% of pixels, and we want to decide the next 1% of “most informative” pixels. Active learning methods are online and sequential in nature. Our goal is to adaptively discover the best sensing mask during acquisition using feedback about the structures in the image. In the end, we hope to recover a high quality reconstruction with a dose reduction relative to the non-adaptive (random) sensing scheme. In doing this, we try three metrics applied to the partial reconstructions for selecting the new set of pixels: (1) variance, (2) Kullback-Leibler (KL) divergence using a Radial Basis Function (RBF) kernel, and (3) entropy. Figs. 1 and 2 display the comparison of Peak Signal-to-Noise (PSNR) using these three different active learning methods at different percentages of sampled pixels. At 20% level, all the three active learning methods underperform the original CS without active learning. However, they all beat the original CS as more of the “most informative” pixels are sampled. One can also argue that CS equipped with active learning requires less sampled pixels to achieve the same value of PSNR than CS with pixels randomly sampled, since all the three PSNR curves with active learning grow at a faster pace than that without active learning. For this particular STEM image, by observing the reconstructed images and the sensing masks, we find that while the method based on RBF kernel acquires samples more uniformly, the one on entropy samples more areas of significant change, thus less uniformly. The KL-divergence method performs the best in terms of reconstruction error (PSNR) for this example [8].

Xie, Weiyi↗
DOE OSTI2014

Lattice Anharmonicity and Thermal Conductivity from Compressive Sensing of First-Principles Calculations

First-principles prediction of lattice thermal conductivity K L of strongly anharmonic crystals is a long-standing challenge in solid state physics. Using recent advances in information science, we propose a systematic and rigorous approach to this problem, compressive sensing lattice dynamics (CSLD). Compressive sensing is used to select the physically important terms in the lattice dynamics model and determine their values in one shot. Non-intuitively, high accuracy is achieved when the model is trained on first-principles forces in quasi-random atomic configurations. The method is demonstrated for Si, NaCl, and Cu 12 Sb 4 S 13 , an earth-abundant thermoelectric with strong phononphonon interactions that limit the room-temperature K L to values near the amorphous limit.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Distinguishing one from many using super-resolution compressive sensing

We present that distinguishing whether a signal corresponds to a single source or a limited number of highly overlapping point spread functions (PSFs) is a ubiquitous problem across all imaging scales, whether detecting receptor-ligand interactions in cells or detecting binary stars. Super-resolution imaging based upon compressed sensing exploits the relative sparseness of the point sources to successfully resolve sources which may be separated by much less than the Rayleigh criterion. However, as a solution to an underdetermined system of linear equations, compressive sensing requires the imposition of constraints which may not always be valid. One typical constraint is that the PSF is known. However, the PSF of the actual optical system may reflect aberrations not present in the theoretical ideal optical system. Even when the optics are well characterized, the actual PSF may reflect factors such as non-uniform emission of the point source (e.g. fluorophore dipole emission). As such, the actual PSF may differ from the PSF used as a constraint. Similarly, multiple different regularization constraints have been suggested including the l 1 -norm, l 0 -norm, and generalized Gaussian Markov random fields (GGMRFs), each of which imposes a different constraint. Other important factors include the signal-to-noise ratio of the point sources and whether the point sources vary in intensity. In this work, we explore how these factors influence super-resolution image recovery robustness, determining the sensitivity and specificity. In conclusion, we determine an approach that is more robust to the types of PSF errors present in actual optical systems.

42 ENGINEERING↗
DOE OSTI2018

Compressive Sensing with Cross-Validation and Stop-Sampling for Sparse Polynomial Chaos Expansions

Here, compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform numerical investigations employing several compressive sensing solvers that target the unconstrained LASSO formulation, with a focus on linear systems that arise in the construction of polynomial chaos expansions. With core solvers l1_ls, SpaRSA, CGIST, FPC_AS, and ADMM, we develop techniques to mitigate overfitting through an automated selection of regularization constant based on cross-validation, and a heuristic strategy to guide the stop-sampling decision. Practical recommendations on parameter settings for these techniques are provided and discussed. The overall method is applied to a series of numerical examples of increasing complexity, including large eddy simulations of supersonic turbulent jet-in-crossflow involving a 24-dimensional input. Through empirical phase-transition diagrams and convergence plots, we illustrate sparse recovery performance under structures induced by polynomial chaos, accuracy, and computational trade-offs between polynomial bases of different degrees, and practicability of conducting compressive sensing for a realistic, high-dimensional physical application. Across test cases studied in this paper, we find ADMM to have demonstrated empirical advantages through consistent lower errors and faster computational times.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Framework of compressive sensing and data compression for 4D-STEM

Four-dimensional Scanning Transmission Electron Microscopy (4D-STEM) is a powerful technique for high-resolution and high-precision materials characterization at multiple length scales, including the characterization of beam-sensitive materials. However, the field of view of 4D-STEM is relatively small, which in absence of live processing is limited by the data size required for storage. Furthermore, the rectilinear scan approach currently employed in 4D-STEM places a resolution- and signal-dependent dose limit for the study of beam sensitive materials. Improving 4D-STEM data and dose efficiency, by keeping the data size manageable while limiting the amount of electron dose, is thus critical for broader applications. Here we introduce a general method for reconstructing 4D-STEM data with subsampling in both real and reciprocal spaces at high fidelity. The approach is first tested on the subsampled datasets created from a full 4D-STEM dataset, and then demonstrated experimentally using random scan in real-space. The same reconstruction algorithm can also be used for compression of 4D-STEM datasets, leading to a large reduction (100 times or more) in data size, while retaining the fine features of 4D-STEM imaging, for crystalline samples.

4D-STEM↗
DOE OSTI2020

Dynamic compressed sensing for real-time tomographic reconstruction

Electron tomography has achieved higher resolution and quality at reduced doses with recent advances in compressed sensing. Compressed sensing (CS) exploits the inherent sparse signal structure to efficiently reconstruct three-dimensional (3D) volumes at the nanoscale from undersampled measurements. However, the process bottlenecks 3D reconstruction with computation times that run from hours to days. Here we demonstrate a framework for dynamic compressed sensing that produces a 3D specimen structure that updates in real-time as new specimen projections are collected. Researchers can begin interpreting 3D specimens as data is collected to facilitate high-throughput and interactive analysis. Using scanning transmission electron microscopy (STEM), we show that dynamic compressed sensing accelerates the convergence speed by ~3-fold while also reducing its error by 27% for a Au/SrTiO 3 nanoparticle specimen. Before a tomography experiment is completed, the 3D tomogram has interpretable structure within ~33% of completion and fine details are visible as early as ~66%. Upon completion of an experiment, a high-fidelity 3D visualization is produced without further delay. Additionally, we report reconstruction parameters that tune data fidelity can be manipulated throughout the computation without re-running the entire process.

47 OTHER INSTRUMENTATION↗
DOE OSTI2015

WE-G-207-04: Non-Local Total-Variation (NLTV) Combined with Reweighted L1-Norm for Compressed Sensing Based CT Reconstruction

Purpose: Compressed sensing (CS) has been used for CT (4DCT/CBCT) reconstruction with few projections to reduce dose of radiation. Total-variation (TV) in L1-minimization (min.) with local information is the prevalent technique in CS, while it can be prone to noise. To address the problem, this work proposes to apply a new image processing technique, called non-local TV (NLTV), to CS based CT reconstruction, and incorporate reweighted L1-norm into it for more precise reconstruction. Methods: TV minimizes intensity variations by considering two local neighboring voxels, which can be prone to noise, possibly damaging the reconstructed CT image. NLTV, contrarily, utilizes more global information by computing a weight function of current voxel relative to surrounding search area. In fact, it might be challenging to obtain an optimal solution due to difficulty in defining the weight function with appropriate parameters. Introducing reweighted L1-min., designed for approximation to ideal L0-min., can reduce the dependence on defining the weight function, therefore improving accuracy of the solution. This work implemented the NLTV combined with reweighted L1-min. by Split Bregman Iterative method. For evaluation, a noisy digital phantom and a pelvic CT images are employed to compare the quality of images reconstructed by TV, NLTV and reweighted NLTV. Results: In both cases, conventional and reweighted NLTV outperform TV min. in signal-to-noise ratio (SNR) and root-mean squared errors of the reconstructed images. Relative to conventional NLTV, NLTV with reweighted L1-norm was able to slightly improve SNR, while greatly increasing the contrast between tissues due to additional iterative reweighting process. Conclusion: NLTV min. can provide more precise compressed sensing based CT image reconstruction by incorporating the reweighted L1-norm, while maintaining greater robustness to the noise effect than TV min.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

Fast electron microscopy via compressive sensing

Various technologies described herein pertain to compressive sensing electron microscopy. A compressive sensing electron microscope includes a multi-beam generator and a detector. The multi-beam generator emits a sequence of electron patterns over time. Each of the electron patterns can include a plurality of electron beams, where the plurality of electron beams is configured to impart a spatially varying electron density on a sample. Further, the spatially varying electron density varies between each of the electron patterns in the sequence. Moreover, the detector collects signals respectively corresponding to interactions between the sample and each of the electron patterns in the sequence.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Magnetic resonance cholangiopancreatography using optimized integrated combination with parallel imaging and compressed sensing technique

Purpose: To assess the combined parallel imaging (PI) and optimized integrated compressed sensing technique (prototype Compressed SENSE) for magnetic resonance cholangiopancreatography (MRCP) compared with conventional MRCP. Methods: This prospective study was approved by our Institutional Review Board, and all patients provided written informed consent. A total of 56 consecutive patients (27 men and 29 women; mean age 67.2 years) underwent breath-hold three-dimensional (3D) MRCP with PI alone (BH-MRCP; acquisition time, 23 s), respiratory-triggered 3D MRCP with PI alone (RT-MRCP; 201 s) and respiratory-triggered 3D MRCP with Compressed SENSE (RT-MRCPcs; 45 s). Relative duct-to-periductal contrast ratios (RCs) of the pancreaticobiliary ducts were calculated for quantitative image analyses. Two radiologists graded the visibility of the pancreaticobiliary ducts, pancreatic cystic lesion, motion artifact, and overall image quality using a five-point rating scale for qualitative image analyses. Theses qualitative and quantitative measurements were then compared among the three sequences. Results: RCs of the common bile duct, right hepatic duct (RHD), left hepatic duct (LHD), and main pancreatic duct at the pancreatic head, body, and tail segments, were significantly higher RT-MRCP, followed by RT-MRCPcs and BH-MRCP (P < 0.001). The visibility of the peripheral RHD and LHD was slightly better in RT-MRCP than in RT-MRCPcs and BH-MRCP (P < 0.001). The visibility of other pancreaticobiliary ducts, pancreatic cystic lesion, motion artifact, and overall image quality were almost comparable among three sequences. Conclusion: The acquisition time was markedly reduced in RT-MRCPcs compared with conventional RT-MRCP while there were significant differences in both quantitative and qualitative analyses, the differences were small enough that the reduced acquisition time makes up for it.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2018

Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification

Compressive-sensing-based uncertainty quantification methods have become a pow- erful tool for problems with limited data. In this paper, we use the sliced inverse regression (SIR) method to provide an initial guess for the alternating direction method, which is used to enhance sparsity of the Hermite polynomial expansion of stochastic state variables. The sparsity improvement increases both the efficiency and accuracy of the compressive-sensing-based uncertainty quantification method. We demonstrate that the initial guess from SIR is more suitable for the cases when the available data is very limited (Algorithm 4). We also propose another algorithm (Algorithm 5) that performs dimension reduction first with sliced inverse regression, then constructs a Hermite polynomial expansion of the reduced model. This method allows us to approximate the statistics accurately with even less available data. Both methods are non-intrusive and require no a priori information of the sparsity of the system. We demonstrate the effectiveness of these two methods (Algorithms 4 and 5) using problems with up to 500 random dimensions.

Yang, Xiu↗
DOE OSTI2013

Gravity Gradiometry: A Novel Application for Compressed Sensing

During the past decade, compressed sensing (CS) has proven to be extremely useful for sparse signal reconstruction. Here the method of CS is applied to fast mass distribution determination based on cold atom gravity gradiometer measurements. Specifically we consider an array of M gradiometers placed around a 2D target area in order to determine the interior mass distribution in cases where the set of (M) sensor measurements under samples the distribution. This was done by assuming that the system’s sparsity comes from the mass distributions only having K non-zero masses, which led to a non-orthogonal basis dictionary. This lack of orthogonality caused interesting behaviors, including weakened noise performance, and breaking of the typical CS motivated logarithmic scaling of required M values for larger K values. However, for low K values M scaled as expected. Modifications to the gravity sensor model to promote orthogonality and test its impact on signal recovery postponed the onset of anomalous scaling; suggesting that lack of orthogonality is the primary cause. While CS works for this sparse, but intrinsically ill-posed problem, this sensor system displayed increased noise sensitivity and a smaller upper bound on the size of recoverable K sets. However, while these limitations decrease CS performance, significant improvements over traditional sensing approaches are still possible.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2016

Compressive sensing super resolution from multiple observations with application to passive millimeter wave images

In this study we propose a novel framework to obtain high resolution images from compressed sensing imaging systems capturing multiple low resolution images of the same scene. The proposed approach of Compressed Sensing Super Resolution (CSSR), combines existing compressed sensing reconstruction algorithms with a low-resolution to high-resolution approach based on the use of a super Gaussian regularization term. The reconstruction alternates between compressed sensing reconstruction and super resolution reconstruction, including registration parameter estimation. The image estimation subproblem is solved using majorization-minimization while the compressed sensing reconstruction becomes an l 1 -minimization subject to a quadratic constraint. The performed experiments on grayscale and synthetically compressed real millimeter wave images, demonstrate the capability of the proposed framework to provide very good quality super resolved images from multiple low resolution compressed acquisitions.

42 ENGINEERING↗
DOE OSTI2024

High‐speed 4‐dimensional scanning transmission electron microscopy using compressive sensing techniques

Abstract 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.

Robinson, Alex W.↗
DOE OSTI2018

An L$_0$L$_1$-norm compressive sensing paradigm for the construction of sparse predictive lattice models using mixed integer quadratic programming

First-principles based lattice models allow the modeling of ab initio thermodynamics of crystalline mixtures for applications such as the construction of phase diagrams and the identification of ground state atomic orderings. The recent development of compressive sensing approaches for the construction of lattice models has further enabled the systematic construction of sparse physical models without the need for human intuition other than requiring the compactness of effective cluster interactions. However, conventional compressive sensing based on L1-norm regularization is strictly only applicable to certain classes of optimization problems and is otherwise not guaranteed to generate optimally sparse and transferable results, so that the method can only be applied to some materials science applications. In this paper, we illustrate a more robust L0L1-norm compressive-sensing method that removes the limitations of conventional compressive sensing and generally results in sparser lattice models that are at least as predictive as those obtained from L1-norm compressive sensing. Apart from the theory, a practical implementation based on state-of-the-art mixed-integer quadratic programming (MIQP) is proposed. The robustness of our methodology is illustrated for four different transition-metal oxides with relevance as battery cathode materials: Li2xTi2(1-x)O2, Li2xNi2yO2, MgxCr2O4, and NaxCrO2. This method provides a practical and robust approach for the construction of sparser and more predictive lattice models, improving on the compressive sensing paradigm and making it applicable to a much broader range of applications.

Huang, W↗
DOE OSTI2012

Application of Compressed Sensing to 2-D Ultrasonic Propagation Imaging System data

The Ultrasonic Propagation Imaging (UPI) System is a unique, non-contact, laser-based ultrasonic excitation and measurement system developed for structural health monitoring applications. The UPI system imparts laser-induced ultrasonic excitations at user-defined locations on a structure of interest. The response of these excitations is then measured by piezoelectric transducers. By using appropriate data reconstruction techniques, a time-evolving image of the response can be generated. A representative measurement of a plate might contain 800x800 spatial data measurement locations and each measurement location might be sampled at 500 instances in time. The result is a total of 640,000 measurement locations and 320,000,000 unique measurements. This is clearly a very large set of data to collect, store in memory and process. The value of these ultrasonic response images for structural health monitoring applications makes tackling these challenges worthwhile. Recently compressed sensing has presented itself as a candidate solution for directly collecting relevant information from sparse, high-dimensional measurements. The main idea behind compressed sensing is that by directly collecting a relatively small number of coefficients it is possible to reconstruct the original measurement. The coefficients are obtained from linear combinations of (what would have been the original direct) measurements. Often compressed sensing research is simulated by generating compressed coefficients from conventionally collected measurements. The simulation approach is necessary because the direct collection of compressed coefficients often requires compressed sensing analog front-ends that are currently not commercially available. The ability of the UPI system to make measurements at user-defined locations presents a unique capability on which compressed measurement techniques may be directly applied. The application of compressed sensing techniques on this data holds the potential to reduce the number of required measurement locations, reduce the time to make measurements, reduce the memory required to store the measurements, and possibly reduce the computational burden to classify the measurements. This work considers the appropriate selection of the signal dictionary used for signal reconstruction, and performs an evaluation of compressed sensing technique's ability to reconstruct ultrasonic images using fewer measurements than would be needed using traditional Nyquist-limited data collection techniques.

42 ENGINEERING↗
DOE OSTI2019

Aperture‐Synthesis Radar Imaging With Compressive Sensing for Ionospheric Research

Abstract Inverse methods involving compressive sensing are tested in the application of two‐dimensional aperture‐synthesis imaging of radar backscatter from field‐aligned plasma density irregularities in the ionosphere. We consider basis pursuit denoising, implemented with the fast iterative shrinkage thresholding algorithm, and orthogonal matching pursuit (OMP) with a wavelet basis in the evaluation. These methods are compared with two more conventional optimization methods rooted in entropy maximization (MaxENT) and adaptive beamforming (linearly constrained minimum variance or often “Capon's Method.”) Synthetic data corresponding to an extended ionospheric radar target are considered. We find that MaxENT outperforms the other methods in terms of its ability to recover imagery of an extended target with broad dynamic range. Fast iterative shrinkage thresholding algorithm performs reasonably well but does not reproduce the full dynamic range of the target. It is also the most computationally expensive of the methods tested. OMP is very fast computationally but prone to a high degree of clutter in this application. We also point out that the formulation of MaxENT used here is very similar to OMP in some respects, the difference being that the former reconstructs the logarithm of the image rather than the image itself from basis vectors extracted from the observation matrix. MaxENT could in that regard be considered a form of compressive sensing.

Hysell, D. L.↗
DOE OSTI2015

TEM Video Compressive Sensing

One of the main limitations of imaging at high spatial and temporal resolution during in-situ TEM experiments is the frame rate of the camera being used to image the dynamic process. While the recent development of direct detectors has provided the hardware to achieve frame rates approaching 0.1ms, the cameras are expensive and must replace existing detectors. In this paper, we examine the use of coded aperture compressive sensing methods [1, 2, 3, 4] to increase the framerate of any camera with simple, low-cost hardware modifications. The coded aperture approach allows multiple sub-frames to be coded and integrated into a single camera frame during the acquisition process, and then extracted upon readout using statistical compressive sensing inversion. Our simulations show that it should be possible to increase the speed of any camera by at least an order of magnitude. Compressive Sensing (CS) combines sensing and compression in one operation, and thus provides an approach that could further improve the temporal resolution while correspondingly reducing the electron dose rate. Because the signal is measured in a compressive manner, fewer total measurements are required. When applied to TEM video capture, compressive imaging couled improve acquisition speed and reduce the electron dose rate. CS is a recent concept, and has come to the forefront due the seminal work of Candès [5]. Since the publication of Candès, there has been enormous growth in the application of CS and development of CS variants. For electron microscopy applications, the concept of CS has also been recently applied to electron tomography [6], and reduction of electron dose in scanning transmission electron microscopy (STEM) imaging [7]. To demonstrate the applicability of coded aperture CS video reconstruction for atomic level imaging, we simulate compressive sensing on observations of Pd nanoparticles and Ag nanoparticles during exposure to high temperatures and other environmental conditions. Figure 1 highlights the results from the Pd nanoparticle experiment. On the left, 10 frames are reconstructed from a single coded frame—the original frames are shown for comparison. On the right a selection of three frames are shown from reconstructions at compression levels 10,20,30. The reconstructions, which are not post-processed, are true to the original and degrade in a straightforward manner. The final choice of compression level will obviously depend on both the temporal and spatial resolution required for a specific imaging task, but the results indicate that an increase in speed of better than an order of magnitude should be possible for all experiments. References: [1] P Llull, X Liao, X Yuan et al. Optics express 21(9), (2013), p. 10526. [2] J Yang, X Yuan, X Liao et al. Image Processing, IEEE Trans 23(11), (2014), p. 4863. [3] X Yuan, J Yang, P Llull et al. In ICIP 2013 (IEEE), p. 14. [4] X Yuan, P Llull, X Liao et al. In CVPR 2014. p. 3318. [5] EJ Candès, J Romberg and T Tao. Information Theory, IEEE Trans 52(2), (2006), p. 489. [6] P Binev, W Dahmen, R DeVore et al. In Modeling Nanoscale Imaging in Electron Microscopy, eds. T Vogt, W Dahmen and P Binev (Springer US), Nanostructure Science and Technology (2012). p. 73. [7] A Stevens, H Yang, L Carin et al. Microscopy 63(1), (2014), pp. 41.

Stevens, Andrew↗