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All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2013

Designing Experiments Through Compressed Sensing

In the following paper, we discuss how to design an ensemble of experiments through the use of compressed sensing. Specifically, we show how to conduct a small number of physical experiments and then use compressed sensing to reconstruct a larger set of data. In order to accomplish this, we organize our results into four sections. We begin by extending the theory of compressed sensing to a finite product of Hilbert spaces. Then, we show how these results apply to experiment design. Next, we develop an efficient reconstruction algorithm that allows us to reconstruct experimental data projected onto a finite element basis. Finally, we verify our approach with two computational experiments.

Young, Joseph G.↗
NASA NTRSDate not supplied

Compressive Sensing Application for Transient Photometric Measurements

Compressive Sensing (CS) is a mathematical theory for simultaneous data acquisition and compression. Natural phenomena may be sparse in some physical or temporal domain. If we exploit this sparsity by applying the technique of CS to obtain information, how do our measurements change as a function of domain and measurement systematics? What are the specific implications for the science and for the sensing infrastructure? In this talk, we will discuss the generalized systematic effects consequent to the application of CS to time-series photometric measurements. We assess implications for observability, sparsification, and information loss in the detection, retrieval and reconstruction process. To study time-series photometry, we explore the field of gravitational microlensing. A source star, typically in the galactic bulge, gets microlensed when there is a precise alignment of a lensing star and its planetary system, with the source star. The microlensed source star changes in flux magnification as the lensing system crosses the precise path of alignment, resulting in a microlensing curve in time domain. A high-cadence, high-resolution system, which uses low power and bandwidth is essential to obtain valuable science measurements. Hence, we discuss application of CS to gravitational microlensing data sets, which in turn can be generalized to any time-ordered photometric measurements.

Asmita Abhay Korde↗
NASA NTRS2022

Compressive Sensing Based Space Flight Instrument Constellation for Measuring Gravitational Microlensing Parallax

In this work, we provide a compressive sensing architecture for implementing on a space based observatory for detecting transient photometric parallax caused by gravitational microlensing events. Compressive sensing (CS) is a simultaneous data acquisition and compression technique, which can greatly reduce on-board resources required for space flight data storage and ground transmission. We simulate microlensing parallax observations using a space observatory constellation, based on CS detectors. Our results show that average CS error is less than 0.5% using 25% Nyquist rate samples. The error at peak magnification time is significantly lower than the error for distinguishing any two microlensing parallax curves at their peak magnification. Thus, CS is an enabling technology for detecting microlensing parallax, without causing any loss in detection accuracy.

compressive sensing↗
DOE OSTI2020

A data-driven approach to sampling matrix selection for compressive sensing

Sampling is a fundamental aspect of any implementation of compressive sensing. Typically, the choice of sampling method is guided by the reconstruction basis. However, this approach can be problematic with respect to certain hardware constraints and is not responsive to domain-specific context. We propose a method for defining an order for a sampling basis that is optimal with respect to capturing variance in data, thus allowing for meaningful sensing at any desired level of compression. We focus on the Walsh-Hadamard sampling basis for its relevance to hardware constraints, but our approach applies to any sampling basis of interest. We illustrate the effectiveness of our method on the Physical Sciences Inc. Fabry-Perot interferometer sensor multispectral dataset, the Johns Hopkins Applied Physics Lab FTIR-based longwave infrared sensor hyperspectral dataset, and a Colorado State University Swiss Ranger depth image dataset. The spectral datasets consist of simulant experiments, including releases of chemicals such as GAA and SF6. We combine our sampling and reconstruction with the adaptive coherence estimator (ACE) and bulk coherence for chemical detection and we incorporate an algorithmic threshold for ACE values to determine the presence or absence of a chemical. We compare results across sampling methods in this context. We have successful chemical detection at a compression rate of 90%. For all three datasets, we compare our sampling approach to standard orderings of sampling basis such as random, sequency, and an analog of sequency that we term `frequency.' In one instance, the peak signal to noise ratio was improved by over 30% across a test set of depth images.

compressive sensing, hyperspectral imaging, Walsh-↗
DOE OSTI2015

Compressed-sensing-based content-driven hierarchical reconstruction: Theory and application to C-arm cone-beam tomography

Purpose: This paper addresses the reconstruction of x-ray cone-beam computed tomography (CBCT) for interventional C-arm systems. Subsampling of CBCT is a significant issue with C-arms due to their slow rotation and to the low frame rate of their flat panel x-ray detectors. The aim of this work is to propose a novel method able to handle the subsampling artifacts generally observed with analytical reconstruction, through a content-driven hierarchical reconstruction based on compressed sensing. Methods: The central idea is to proceed with a hierarchical method where the most salient features (high intensities or gradients) are reconstructed first to reduce the artifacts these features induce. These artifacts are addressed first because their presence contaminates less salient features. Several hierarchical schemes aiming at streak artifacts reduction are introduced for C-arm CBCT: the empirical orthogonal matching pursuit approach with the ℓ{sub 0} pseudonorm for reconstructing sparse vessels; a convex variant using homotopy with the ℓ{sub 1}-norm constraint of compressed sensing, for reconstructing sparse vessels over a nonsparse background; homotopy with total variation (TV); and a novel empirical extension to nonlinear diffusion (NLD). Such principles are implemented with penalized iterative filtered backprojection algorithms. For soft-tissue imaging, the authors compare the use of TV and NLD filters as sparsity constraints, both optimized with the alternating direction method of multipliers, using a threshold for TV and a nonlinear weighting for NLD. Results: The authors show on simulated data that their approach provides fast convergence to good approximations of the solution of the TV-constrained minimization problem introduced by the compressed sensing theory. Using C-arm CBCT clinical data, the authors show that both TV and NLD can deliver improved image quality by reducing streaks. Conclusions: A flexible compressed-sensing-based algorithmic approach is proposed that is able to accommodate for a wide range of constraints. It is successfully applied to C-arm CBCT images that may not be so well approximated by piecewise constant functions.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Analysis of the ratio of ℓ 1 and ℓ 2 norms in compressed sensing

We study the ratio of ℓ 1 and ℓ 2 norms ( ℓ 1 / ℓ 2 ) as a sparsity-promoting objective in compressed sensing. We first propose a novel criterion that guarantees that an s-sparse signal is the local minimizer of the ℓ 1 / ℓ 2 objective; our criterion is interpretable and useful in practice. We also give the first uniform recovery condition using a geometric characterization of the null space of the measurement matrix, and show that this condition is satisfied for a class of random matrices. We also present analysis on the robustness of the procedure when noise pollutes data. Numerical experiments are provided that compare ℓ 1 / ℓ 2 with some other popular non-convex methods in compressed sensing. Finally, we propose a novel initialization approach to accelerate the numerical optimization procedure. We call this initialization approach support selection, and we demonstrate that it empirically improves the performance of existing ℓ 1 / ℓ 2 algorithms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Next Steps for Compressively Sensed Video in Transmission Electron Microscopy

Here, compressive sensing (CS) is a fast-emerging approach for improving data throughput by taking advantage of the inherent compressibility of real world data—the same kind of compressibility that allows millions of users to stream full-screen video without breaking the internet. Transmission electron microscope (TEM) users regularly collect multi-GB data sets and then use aggressive data reduction strategies to draw out the tiny residual of Shannon entropy that answers the question they wanted to ask. Much of the raw-byte-count information in an acquisition is random, redundant, or irrelevant, yet its collection still represents substantial cost in terms of instrumentation bandwidth and sample damage.

47 OTHER INSTRUMENTATION↗
NASA NTRS2016

Application of Compressive Sensing to Gravitational Microlensing Data and Implications for Miniaturized Space Observatories

Compressive Sensing is a technique for simultaneous acquisition and compression of data that is sparse or can be made sparse in some domain. It is currently under intense development and has been profitably employed for industrial and medical applications. We here describe the use of this technique for the processing of astronomical data. We outline the procedure as applied to exoplanet gravitational microlensing and analyze measurement results and uncertainty values. We describe implications for on-spacecraft data processing for space observatories. Our findings suggest that application of these techniques may yield significant, enabling benefits especially for power and volume-limited space applications such as miniaturized or micro-constellation satellites.

Gravitational Microlensing↗
NASA NTRS2016

Application of Compressive Sensing to Gravitational Microlensing Data and Implications for Miniaturized Space Observatories

Compressive Sensing is a technique for simultaneous acquisition and compression of data that is sparse or can be made sparse in some domain. It is currently under intense development and has been profitably employed for industrial and medical applications. We here describe the use of this technique for the processing of astronomical data. We outline the procedure as applied to exoplanet gravitational microlensing and analyze measurement results and uncertainty values. We describe implications for on-spacecraft data processing for space observatories. Our findings suggest that application of these techniques may yield significant, enabling benefits especially for power and volume-limited space applications such as miniaturized or micro-constellation satellites.

Compressive Sensing↗
DOE OSTI2016

A Comparison of Compressed Sensing and Sparse Recovery Algorithms Applied to Simulation Data

The move toward exascale computing for scientific simulations is placing new demands on compression techniques. It is expected that the I/O system will not be able to support the volume of data that is expected to be written out. To enable quantitative analysis and scientific discovery, we are interested in techniques that compress high-dimensional simulation data and can provide perfect or near-perfect reconstruction. In this paper, we explore the use of compressed sensing (CS) techniques to reduce the size of the data before they are written out. Using large-scale simulation data, we investigate how the sufficient sparsity condition and the contrast in the data affect the quality of reconstruction and the degree of compression. Also, we provide suggestions for the practical implementation of CS techniques and compare them with other sparse recovery methods. Finally, our results show that despite longer times for reconstruction, compressed sensing techniques can provide near perfect reconstruction over a range of data with varying sparsity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Temporal compressive sensing systems

Methods and systems for temporal compressive sensing are disclosed, where within each of one or more sensor array data acquisition periods, one or more sensor array measurement datasets comprising distinct linear combinations of time slice data are acquired, and where mathematical reconstruction allows for calculation of accurate representations of the individual time slice datasets.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Temporal compressive sensing systems

Methods and systems for temporal compressive sensing are disclosed, where within each of one or more sensor array data acquisition periods, one or more sensor array measurement datasets comprising distinct linear combinations of time slice data are acquired, and where mathematical reconstruction allows for calculation of accurate representations of the individual time slice datasets.

47 OTHER INSTRUMENTATION↗
DOE OSTI2020

Temporal compressive sensing systems

Methods and systems for temporal compressive sensing are disclosed, where within each of one or more sensor array data acquisition periods, one or more sensor array measurement datasets comprising distinct linear combinations of time slice data are acquired, and where mathematical reconstruction allows for calculation of accurate representations of the individual time slice datasets.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2019

Electrostatic subframing and compressive-sensing video in transmission electron microscopy

We present kilohertz-scale video capture rates in a transmission electron microscope, using a camera normally limited to hertz-scale acquisition. An electrostatic deflector rasters a discrete array of images over a large camera, decoupling the acquisition time per subframe from the camera readout time. Total-variation regularization allows features in overlapping subframes to be correctly placed in each frame. Moreover, the system can be operated in a compressive-sensing video mode, whereby the deflections are performed in a known pseudorandom sequence. Compressive sensing in effect performs data compression before the readout, such that the video resulting from the reconstruction can have substantially more total pixels than that were read from the camera. This allows, for example, 100 frames of video to be encoded and reconstructed using only 15 captured subframes in a single camera exposure. We demonstrate experimental tests including laser-driven melting/dewetting, sintering, and grain coarsening of nanostructured gold, with reconstructed video rates up to 10 kHz. The results exemplify the power of the technique by showing that it can be used to study the fundamentally different temporal behavior for the three different physical processes. Both sintering and coarsening exhibited self-limiting behavior, whereby the process essentially stopped even while the heating laser continued to strike the material. We attribute this to changes in laser absorption and to processes inherent to thin-film coarsening. In contrast, the dewetting proceeded at a relatively uniform rate after an initial incubation time consistent with the establishment of a steady-state temperature profile.

36 MATERIALS SCIENCE↗
NASA NTRSDate not supplied

Compressive Sensing Based Data Acquisition Architecture for Transient Stellar Events in Crowded Star Fields

Compressive sensing is a mathematical technique for simultaneous data acquisition and compression. In this work, we show a CS based architecture for acquiring and reconstructing transient stellar events. This architecture recon-structs a differenced image itself, eliminating the need for any sparse domain transforms, otherwise required for traditional CS reconstruction. The resulting reconstructed differenced image is of critical importance as the information required for generating a time-series photometric light curve is obtained only from a differenced image. Hence, reconstructing a crowded star spatial image, followed by differencing is wasteful. This architecture eliminates the need to 1.) transform an image to a sparse domain, 2.) Reconstruct a dense field, and then apply differencing on the image to obtain the image of critical value. We study the case of microlensing to depict a star source experiencing magnification in time. Our results show that this architecture is able to reconstruct star source magnitudes with magnification factors greater than 1 for clean images with error less than 2% using only 10% of the Nyquist rate samples.

Compressive Sensing, Data acquisition, Image diffe↗