scholarly journals Reconstruction algorithms for low-rank tensors and depth-3 multilinear circuits

2021 ◽  
Author(s):  
Vishwas Bhargava ◽  
Shubhangi Saraf ◽  
Ilya Volkovich
Keyword(s):  
Low Rank ◽  
Reconstruction Algorithms

scholarly journals Recovering spectral images from compressive measurements using designed coded apertures and Matrix Completion Theory

2017 ◽  
Vol 21 (2) ◽  
Author(s):  
Tatiana Gelvez ◽  
Hoover Rueda ◽  
Henry Arguello
Keyword(s):  
Imaging Techniques ◽  
Matrix Completion ◽  
Spectral Imaging ◽  
Spatial Location ◽  
Low Rank ◽  
Coded Aperture ◽  
Reconstruction Algorithms ◽  
Spectral Image ◽  
The Matrix ◽  
Spectral Imager

<p>Spectral imaging aims to capture and process a 3-dimensional spectral image with a large amount of spectral information for each spatial location. Compressive spectral imaging techniques (CSI) increases the sensing speed and reduces the amount of collected data compared to traditional spectral imaging methods. The coded aperture snapshot spectral imager (CASSI) is an optical architecture to sense a spectral image in a single 2D coded projection by applying CSI. Typically, the 3D scene is recovered by solving an L1-based optimization problem that assumes the scene is sparse in some known orthonormal basis. In contrast, the matrix completion technique (MC) allows to recover the scene without such prior knowledge. The MC reconstruction algorithms rely on a low-rank structure of the scene. Moreover, the CASSI system uses coded aperture patterns that determine the quality of the estimated scene. Therefore, this paper proposes the design of an optimal coded aperture set for the MC methodology. The designed set is attained by maximizing the distance between the translucent elements in the coded aperture. Visualization of the recovered spectral signals and simulations over different databases show average improvement when the designed coded set is used between 1-3 dBs compared to the complementary coded aperture set, and between 3-9 dBs compared to the conventional random coded aperture set.</p>

scholarly journals Quantization for low-rank matrix recovery

2018 ◽  
Vol 8 (1) ◽  
pp. 161-180
Author(s):  
Eric Lybrand ◽  
Rayan Saab
Keyword(s):  
Compressed Sensing ◽  
Reconstruction Error ◽  
Linear Operators ◽  
Low Rank ◽  
Quantization Scheme ◽  
Reconstruction Algorithms ◽  
Finite Frame ◽  
Rank Matrix ◽  
Band Limited ◽  
Low Rank Matrix

Abstract We study Sigma–Delta $(\varSigma\!\varDelta) $ quantization methods coupled with appropriate reconstruction algorithms for digitizing randomly sampled low-rank matrices. We show that the reconstruction error associated with our methods decays polynomially with the oversampling factor, and we leverage our results to obtain root-exponential accuracy by optimizing over the choice of quantization scheme. Additionally, we show that a random encoding scheme, applied to the quantized measurements, yields a near-optimal exponential bit rate. As an added benefit, our schemes are robust both to noise and to deviations from the low-rank assumption. In short, we provide a full generalization of analogous results, obtained in the classical setup of band-limited function acquisition, and more recently, in the finite frame and compressed sensing setups to the case of low-rank matrices sampled with sub-Gaussian linear operators. Finally, we believe our techniques for generalizing results from the compressed sensing setup to the analogous low-rank matrix setup is applicable to other quantization schemes.

scholarly journals Guaranteed recovery of quantum processes from few measurements

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 171 ◽  
Author(s):  
Martin Kliesch ◽  
Richard Kueng ◽  
Jens Eisert ◽  
David Gross
Keyword(s):  
A Priori ◽  
Measurement Model ◽  
Low Rank ◽  
Quantum Channels ◽  
Reconstruction Algorithms ◽  
Quantum Processes ◽  
Quantum Process ◽  
Multiple Channel ◽  
Quantum Process Tomography ◽  
Process Tomography

Quantum process tomography is the task of reconstructing unknown quantum channels from measured data. In this work, we introduce compressed sensing-based methods that facilitate the reconstruction of quantum channels of low Kraus rank. Our main contribution is the analysis of a natural measurement model for this task: We assume that data is obtained by sending pure states into the channel and measuring expectation values on the output. Neither ancillary systems nor coherent operations across multiple channel uses are required. Most previous results on compressed process reconstruction reduce the problem to quantum state tomography on the channel's Choi matrix. While this ansatz yields recovery guarantees from an essentially minimal number of measurements, physical implementations of such schemes would typically involve ancillary systems. A priori, it is unclear whether a measurement model tailored directly to quantum process tomography might require more measurements. We establish that this is not the case.Technically, we prove recovery guarantees for three different reconstruction algorithms. The reconstructions are based on a trace, diamond, and ℓ2-norm minimization, respectively. Our recovery guarantees are uniform in the sense that with one random choice of measurement settings all quantum channels can be recovered equally well. Moreover, stability against arbitrary measurement noise and robustness against violations of the low-rank assumption is guaranteed. Numerical studies demonstrate the feasibility of the approach.

Three dimensional deblurring of transmitted-light brightfield micrographs

1993 ◽  
Vol 51 ◽  
pp. 564-565
Author(s):  
Santosh Bhattacharyya
Keyword(s):  
Image Reconstruction ◽  
Three Dimensional ◽  
Transmitted Light ◽  
Reconstruction Algorithms ◽  
3D Image Reconstruction ◽  
Structural Details ◽  
Spread Function ◽  
Early Testing ◽  
Linearized Model ◽  
Image Reconstruction Algorithms

Three dimensional microscopic structures play an important role in the understanding of various biological and physiological phenomena. Structural details of neurons, such as the density, caliber and volumes of dendrites, are important in understanding physiological and pathological functioning of nervous systems. Even so, many of the widely used stains in biology and neurophysiology are absorbing stains, such as horseradish peroxidase (HRP), and yet most of the iterative, constrained 3D optical image reconstruction research has concentrated on fluorescence microscopy. It is clear that iterative, constrained 3D image reconstruction methodologies are needed for transmitted light brightfield (TLB) imaging as well. One of the difficulties in doing so, in the past, has been in determining the point spread function of the system.We have been developing several variations of iterative, constrained image reconstruction algorithms for TLB imaging. Some of our early testing with one of them was reported previously. These algorithms are based on a linearized model of TLB imaging.

The Influences of the Rank of Coal on Methane Sorption Capacity in Coals/Wpływ Rzędu Węgla Na Pojemność Sorpcyjną Metanu W Węglach

2014 ◽  
Vol 59 (2) ◽  
pp. 509-516
Author(s):  
Andrzej Olajossy
Keyword(s):  
Sorption Capacity ◽  
Coalbed Methane ◽  
Vitrinite Reflectance ◽  
Sorption Isotherms ◽  
Volatile Matter ◽  
Low Rank ◽  
Hard Coal ◽  
Petrographic Composition ◽  
Methane Sorption ◽  
Indian Coals

Abstract Methane sorption capacity is of significance in the issues of coalbed methane (CBM) and depends on various parameters, including mainly, on rank of coal and the maceral content in coals. However, in some of the World coals basins the influences of those parameters on methane sorption capacity is various and sometimes complicated. Usually the rank of coal is expressed by its vitrinite reflectance Ro. Moreover, in coals for which there is a high correlation between vitrinite reflectance and volatile matter Vdaf the rank of coal may also be represented by Vdaf. The influence of the rank of coal on methane sorption capacity for Polish coals is not well understood, hence the examination in the presented paper was undertaken. For the purpose of analysis there were chosen fourteen samples of hard coal originating from the Upper Silesian Basin and Lower Silesian Basin. The scope of the sorption capacity is: 15-42 cm3/g and the scope of vitrinite reflectance: 0,6-2,2%. Majority of those coals were of low rank, high volatile matter (HV), some were of middle rank, middle volatile matter (MV) and among them there was a small number of high rank, low volatile matter (LV) coals. The analysis was conducted on the basis of available from the literature results of research of petrographic composition and methane sorption isotherms. Some of those samples were in the form (shape) of grains and others - as cut out plates of coal. The high pressure isotherms previously obtained in the cited studies were analyzed here for the purpose of establishing their sorption capacity on the basis of Langmuire equation. As a result of this paper, it turned out that for low rank, HV coals the Langmuire volume VL slightly decreases with the increase of rank, reaching its minimum for the middle rank (MV) coal and then increases with the rise of the rank (LV). From the graphic illustrations presented with respect to this relation follows the similarity to the Indian coals and partially to the Australian coals.

Technology for firing low rank of gaseous fuel based on multistage preheating by recirculated hot flue gas

2014 ◽  
Author(s):  
An Wang ◽  
Donglin Chen ◽  
Shan Cheng ◽  
Xuepeng Jiao ◽  
Wenwei Chen
Keyword(s):  
Flue Gas ◽  
Gaseous Fuel ◽  
Low Rank

A low-rank nonlinear ensemble filter for vortex models of aerodynamic flows

2021 ◽  
Author(s):  
Mathieu Le Provost ◽  
Ricardo Baptista ◽  
Youssef Marzouk ◽  
Jeff Eldredge
Keyword(s):  
Low Rank ◽  
Aerodynamic Flows

X-Ray Nanotomography (XRMT) Tool for Non-Destructive High-Resolution Imaging of ICs

2001 ◽  
Author(s):  
Wenbing Yun ◽  
Steve Wang ◽  
David Scott ◽  
Kenneth W. Nill ◽  
Waleed S. Haddad
Keyword(s):  
High Resolution ◽  
Process Development ◽  
3D Visualization ◽  
Tomographic Reconstruction ◽  
Reconstruction Algorithms ◽  
X Ray ◽  
Visualization Software ◽  
Volumetric Reconstruction ◽  
Resolution Imaging ◽  
Non Destructive

Abstract A high-resolution table-sized x-ray nanotomography (XRMT) tool has been constructed that shows the promise of nondestructively imaging the internal structure of a full IC stack with a spatial resolution better than 100 nm. Such a tool can be used to detect, localize, and characterize buried defects in the IC. By collecting a set of X-ray projections through the full IC (which may include tens of micrometers of silicon substrate and several layers of Cu interconnects) and applying tomographic reconstruction algorithms to these projections, a 3D volumetric reconstruction can be obtained, and analyzed for defects using 3D visualization software. XRMT is a powerful technique that will find use in failure analysis and IC process development, and may facilitate or supplant investigations using SEM, TEM, and FIB tools, which generally require destructive sample preparation and a vacuum environment.

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