Computation Of Covariance Matrix Research Articles

Software Tool for Soil Surface Parameters Retrieval from Fully Polarimetric Remotely Sensed SAR Data.

The retrieval of soil surface parameters, in particular soil moisture and roughness, based on Synthetic Aperture Radar (SAR) data, has been the subject of a large number of studies, of which results are available in the scientific literature. However, although refined methods based on theoretical/analytical scattering models have been proposed and successfully applied in experimental studies, at the operative level very simple, empirical models with a number of adjustable parameters are usually employed. One of the reasons for this situation is that retrieval methods based on analytical scattering models are not easy to implement and to be employed by non-expert users. Related to this, commercially and freely available software tools for the processing of SAR data, although including routines for basic manipulation of polarimetric SAR data (e.g., coherency and covariance matrix calculation, Pauli decomposition, etc.), do not implement easy-to-use methods for surface parameter retrieval. In order to try to fill this gap, in this paper we present a user-friendly computer program for the retrieval of soil surface parameters from Polarimetric Synthetic Aperture Radar (PolSAR) imageries. The program evaluates soil permittivity, soil moisture and soil roughness based on the theoretical predictions of the electromagnetic scattering provided by the Polarimetric Two-Scale Model (PTSM) and the Polarimetric Two-Scale Two-Component Model (PTSTCM). In particular, nine different retrieval methodologies, whose applicability depends on both the used polarimetric data (dual- or full-pol) and the characteristics of the observed scene (e.g., on its topography and on its vegetation cover), as well as their implementation in the Interactive Data Language (IDL) platform, are discussed. One specific example from Germany’s Demmin test-site is presented in detail, in order to provide a first guide to the use of the tool. Obtained retrieval results are in agreement with what was expected according to the available literature.

Low-complexity adaptive minimum variance ultrasound beam-former based on diagonalization

BackgroundDespite the high capability of the minimum variance (MV) beam-former in improving image quality compared to the delay and sum (DAS), its high complexity, which is due to L × L covariance matrix inversion and calculation, limits its usage for real-time applications. The complexity of MV is in the order of O(L3). MethodA low-complexity adaptive MV (LCAMV) is suggested in to reduce the complexity of the MV beam-former via the covariance matrix diagonalization. So, the proposed method focuses on two aspects: One is to reduce the complexity due to covariance matrix calculation and the other to reduce the MV complexity caused by the inversion. Thus, the MV complexity is significantly reduced, although the resulted image of LCAMV is similar to that of MV. ResultsThe LCAMV technique is applied to the simulated phantoms and real data to verify its performance and to compare it with other popular beamforming techniques. Statistical parameters of the image quality for all experiments were calculated to check the image quality. Also, the run time analysis showed that the difference between the values of the MV and LCAMV statistical image quality parameters was less than 2%, while the speed of LCAMV was about 4 times faster. ConclusionResults indicate that using LCAMV, not only the resolution and contrast are not changed significantly, but also the complexity is reduced from O(L3) to O(L×log(L)). Thus, this simple technique can be a big step towards adaptive real-time imaging.

2D-FFTLog: efficient computation of real-space covariance matrices for galaxy clustering and weak lensing

ABSTRACT Accurate covariance matrices for two-point functions are critical for inferring cosmological parameters in likelihood analyses of large-scale structure surveys. Among various approaches to obtaining the covariance, analytic computation is much faster and less noisy than estimation from data or simulations. However, the transform of covariances from Fourier space to real space involves integrals with two Bessel integrals, which are numerically slow and easily affected by numerical uncertainties. Inaccurate covariances may lead to significant errors in the inference of the cosmological parameters. In this paper, we introduce a 2D-FFTLog algorithm for efficient, accurate, and numerically stable computation of non-Gaussian real-space covariances for both 3D and projected statistics. The 2D-FFTLog algorithm is easily extended to perform real-space bin-averaging. We apply the algorithm to the covariances for galaxy clustering and weak lensing for a Dark Energy Survey Year 3-like and a Rubin Observatory’s Legacy Survey of Space and Time Year 1-like survey, and demonstrate that for both surveys, our algorithm can produce numerically stable angular bin-averaged covariances with the flat sky approximation, which are sufficiently accurate for inferring cosmological parameters. The code CosmoCov for computing the real-space covariances with or without the flat-sky approximation is released along with this paper.

Learning nonlinear turbulent dynamics from partial observations via analytically solvable conditional statistics

Learning nonlinear turbulent dynamics from partial observations is an important and challenging topic. In this article, an efficient learning algorithm based on the expectation-maximization approach is developed for a rich class of complex nonlinear turbulent dynamics using short training data. Despite the significant nonlinear and non-Gaussian features in these models, the analytically solvable conditional statistics allows the development of an exact and accurate nonlinear optimal smoother for recovering the hidden variables, which facilitates an efficient learning of these fully nonlinear models with extreme events. Then three additional ingredients are incorporated into the basic algorithm for improving the learning process. First, the physics constraint that requires the conservation of energy in the quadratic nonlinear terms is taken into account. It plays an important role in preventing the finite-time blowup of the solution and various pathological behavior of the recovered model. Second, a judicious block decomposition is applied to many large-dimensional nonlinear systems. It greatly accelerates the calculation of high-dimensional conditional covariance matrix and provides an extremely cheap parallel computation for learning the model parameters. Third, sparse identification of the complex turbulent models is combined with the learning algorithm that leads to parsimonious models. Numerical tests show the skill of the algorithm in learning the nonlinear dynamics and non-Gaussian statistics with extreme events in both perfect model and model error scenarios. It is also shown that in the presence of noise and partial observations, the model is not uniquely identified. Different nonlinear models all perfectly capture the key non-Gaussian features and obtain the same ensemble forecast skill of the observed variables as the perfect model, but they may have distinct model responses to external perturbations.

Single-Pass Covariance Matrix Calculation on a Hybrid FPGA/CPU Platform

Covariance matrices are used for a wide range of applications in particle physics, including Kálmán filter for tracking purposes or Primary Component Analysis for dimensionality reduction. Based on a novel decomposition of the covariance matrix, a design that requires only one pass of data for calculating the covariance matrix is presented. Two computation engines are used depending on parallelizability of the necessary computation steps. The design is implemented onto a hybrid FPGA/CPU system and yields speed-up of up to 5 orders of magnitude compared to previous FPGA implementation.

Deep Kernel and Deep Learning for Genome-Based Prediction of Single Traits in Multienvironment Breeding Trials.

Deep learning (DL) is a promising method for genomic-enabled prediction. However, the implementation of DL is difficult because many hyperparameters (number of hidden layers, number of neurons, learning rate, number of epochs, batch size, etc.) need to be tuned. For this reason, deep kernel methods, which only require defining the number of layers, may be an attractive alternative. Deep kernel methods emulate DL models with a large number of neurons, but are defined by relatively easily computed covariance matrices. In this research, we compared the genome-based prediction of DL to a deep kernel (arc-cosine kernel, AK), to the commonly used non-additive Gaussian kernel (GK), as well as to the conventional additive genomic best linear unbiased predictor (GBLUP/GB). We used two real wheat data sets for benchmarking these methods. On average, AK and GK outperformed DL and GB. The gain in terms of prediction performance of AK and GK over DL and GB was not large, but AK and GK have the advantage that only one parameter, the number of layers (AK) or the bandwidth parameter (GK), has to be tuned in each method. Furthermore, although AK and GK had similar performance, deep kernel AK is easier to implement than GK, since the parameter “number of layers” is more easily determined than the bandwidth parameter of GK. Comparing AK and DL for the data set of year 2015–2016, the difference in performance of the two methods was bigger, with AK predicting much better than DL. On this data, the optimization of the hyperparameters for DL was difficult and the finally used parameters may have been suboptimal. Our results suggest that AK is a good alternative to DL with the advantage that practically no tuning process is required.

Clutter Suppression via Subspace Projection for Spaceborne HRWS Multichannel SAR System

Traditional clutter suppression methods are mainly studied under the condition that the pulse repetition frequency (PRF) of the system is not less than the Nyquist frequency. Whereas in the high-resolution and wide-swath (HRWS) multichannel synthetic aperture radar (SAR) system, a low PRF is used to break through the minimum antenna area constraint. The low PRF case brings new challenges to the traditional clutter suppression methods. In this letter, a subspace projection clutter suppression method is proposed based on the fact that moving targets and the clutter consist in different signal subspaces. This method can be directly applied to the HRWS multichannel SAR system, and it shows better performance compared to the space-time adaptive processing (STAP) when the moving target components cannot be ignored in the clutter covariance matrix calculation. Simulated data and airborne measured data are processed to verify its effectiveness.

Cosmology with stacked cluster weak lensing and cluster–galaxy cross-correlations

ABSTRACT Cluster weak lensing is a sensitive probe of cosmology, particularly the amplitude of matter clustering σ8 and matter density parameter Ωm. The main nuisance parameter in a cluster weak lensing cosmological analysis is the scatter between the true halo mass and the relevant cluster observable, denoted $\sigma _{\ln M_\mathrm{ c}}$. We show that combining the cluster weak lensing observable ΔΣ with the projected cluster–galaxy cross-correlation function wp,cg and galaxy autocorrelation function wp,gg can break the degeneracy between σ8 and $\sigma _{\ln M_\mathrm{ c}}$ to achieve tight, per cent-level constraints on σ8. Using a grid of cosmological N-body simulations, we compute derivatives of ΔΣ, wp,cg, and wp,gg with respect to σ8, Ωm, $\sigma _{\ln M_\mathrm{ c}}$, and halo occupation distribution (HOD) parameters describing the galaxy population. We also compute covariance matrices motivated by the properties of the Dark Energy Survey cluster and weak lensing survey and the BOSS CMASS galaxy redshift survey. For our fiducial scenario combining ΔΣ, wp,cg, and wp,gg measured over 0.3−30.0 h−1 Mpc, for clusters at z = 0.35−0.55 above a mass threshold Mc ≈ 2 × 1014 h−1 M⊙, we forecast a $1.4{{\ \rm per\ cent}}$ constraint on σ8 while marginalizing over $\sigma _{\ln M_\mathrm{ c}}$ and all HOD parameters. Reducing the mass threshold to 1 × 1014 h−1 M⊙ and adding a z = 0.15−0.35 redshift bin sharpens this constraint to $0.8{{\ \rm per\ cent}}$. The small-scale (rp < 3.0 h−1 Mpc) ‘mass function’ and large-scale (rp > 3.0 h−1 Mpc) ‘halo-mass cross-correlation’ regimes of ΔΣ have comparable constraining power, allowing internal consistency tests from such an analysis.

Fast Computation of Single Scattering in Participating Media with Refractive Boundaries Using Frequency Analysis.

Many materials combine a refractive boundary and a participating media on the interior. If the material has a low opacity, single scattering effects dominate in its appearance. Refraction at the boundary concentrates the incoming light, resulting in an important phenomenon called volume caustics. This phenomenon is hard to simulate. Previous methods used point-based light transport, but attributed point samples inefficiently, resulting in long computation time. In this paper, we use frequency analysis of light transport to allocate point samples efficiently. Our method works in two steps: in the first step, we compute volume samples along with their covariance matrices, encoding the illumination frequency content in a compact way. In the rendering step, we use the covariance matrices to compute the kernel size for each volume sample: small kernel for high-frequency single scattering, large kernel for lower frequencies. Our algorithm computes volume caustics with fewer volume samples, with no loss of quality. Our method is both faster and uses less memory than the original method. It is roughly twice as fast and uses one fifth of the memory. The extra cost of computing covariance matrices for frequency information is negligible.

Developing Computationally Efficient Nonlinear Cubature Kalman Filtering for Visual Inertial Odometry

This paper presents a computationally efficient sensor-fusion algorithm for visual inertial odometry (VIO). The paper utilizes trifocal tensor geometry (TTG) for visual measurement model and a nonlinear deterministic-sampling-based filter known as cubature Kalman filter (CKF) to handle the system nonlinearity. The TTG-based approach is developed to replace the computationally expensive three-dimensional-feature-point reconstruction in the conventional VIO system. This replacement has simplified the system architecture and reduced the processing time significantly. The CKF is formulated for the VIO problem, which helps to achieve a better estimation accuracy and robust performance than the conventional extended Kalman filter (EKF). This paper also addresses the computationally efficient issue associated with Kalman filtering structure using cubature information filter (CIF), the CKF version on information domain. The CIF execution avoids the inverse computation of the high-dimensional innovation covariance matrix, which in turn further improves the computational efficiency of the VIO system. Several experiments use the publicly available datasets for validation and comparing against many other VIO algorithms available in the recent literature. Overall, this proposed algorithm can be implemented as a fast VIO solution for high-speed autonomous robotic systems.

Toward Improving Short‐Term Predictions of Fine Particulate Matter Over the United States Via Assimilation of Satellite Aerosol Optical Depth Retrievals

AbstractThis study develops a new approach to improve simulations of the particulate matter of aerodynamic diameter smaller than 2.5 μm (PM2.5) in the Community Multiscale Air Quality (CMAQ) model via assimilation of Moderate Resolution Imaging Spectroradiometer (MODIS) aerosol optical depth (AOD) retrievals using the Gridpoint Statistical Interpolation (GSI) system. In contrast to previous studies that only consider errors due to transport, our computation of the background error covariance matrix incorporates uncertainties in anthropogenic emissions. To understand the impact of this approach, three experiments (one background and two assimilations) are performed over the contiguous United States (CONUS) from 15 July to 14 August 2014. The background CMAQ experiment significantly underestimates both the MODIS AOD and surface PM2.5 levels. MODIS AOD assimilation pushes both the CMAQ AOD and surface PM2.5 distributions toward the observed distributions, but CMAQ still underestimates the observations. Averaged over CONUS, the two assimilation experiments with and without including the anthropogenic emission uncertainties improve the correlation coefficient between the model and independent observations of PM2.5 by ~67% and ~48%, respectively, and reduces the mean bias by ~38% and ~10%, respectively. The assimilation improves the model performance everywhere over CONUS, except the New York and Wisconsin, where CMAQ overestimates the observed PM2.5 during nighttime after assimilation likely because of overcorrection of aerosol mass concentrations by the AOD assimilation. Future work should incorporate uncertainties in other processes (biomass burning and biogenic emissions, deposition, chemistry, transport, and boundary conditions) to further enhance the value of assimilating spaceborne AOD retrievals.

Geometrical compression: a new method to enhance the BOSS galaxy bispectrum monopole constraints

ABSTRACT We present a novel method to compress galaxy clustering three-point statistics and apply it to redshift space galaxy bispectrum monopole measurements from BOSS DR12 CMASS data considering a k-space range of $0.03-0.12\, h/\mathrm{Mpc}$. The method consists in binning together bispectra evaluated at sets of wavenumbers forming closed triangles with similar geometrical properties: the area, the cosine of the largest angle, and the ratio between the cosines of the remaining two angles. This enables us to increase the number of bispectrum measurements, for example by a factor of 23 over the standard binning (from 116 to 2734 triangles used), which is otherwise limited by the number of mock catalogues available to estimate the covariance matrix needed to derive parameter constraints. The $68{{\ \rm per\ cent}}$ credible intervals for the inferred parameters (b1, b2, f, σ8) are thus reduced by $\left(-39{{\ \rm per\ cent}},-49{{\ \rm per\ cent}},-29{{\ \rm per\ cent}},-22{{\ \rm per\ cent}}\right)$, respectively. We find very good agreement with the posteriors recently obtained by alternative maximal compression methods. This new method does not require the a-priori computation of the data vector covariance matrix and has the potential to be directly applicable to other three-point statistics (e.g. galaxy clustering, weak gravitational lensing, 21-cm emission line) measured from future surveys such as DESI, Euclid, PFS, and SKA.

High-Speed Visual Target Identification for Low-Cost Wearable Brain-Computer Interfaces

Non-invasive brain-computer interfaces (BCI) have received a great deal of attention due to recent advances in signal processing. Two types of electroencephalograms (EEG), P300 and steady-state visual evoked potential (SSVEP), have been widely used to enable paralyzed patients to communicate with others. Although there have been many signal processing algorithms focusing on target identification accuracies such as power spectral density analysis (PSDA) and canonical correlation analysis (CCA), their high computational complexity drives up the cost of such systems. In the proposed lightweight target identification algorithm, we have focused on developing an improved information transfer rate (ITR) for high-quality communication and reducing overall implementation cost. The proposed algorithm, CCA-Lite, includes two algorithmic optimizations–signal binarization and on-the-fly covariance matrix calculation–which have enabled the development of a low-cost, single-channel, and wearable BCI system using SSVEP. The prototypical BCI system makes use of an ARM Cortex-M3-based low-cost microcontroller unit (MCU), which has been built for 1.5s SSVEP recordings. Compared to the state-of-the-art CCA-based target identification algorithm, CCA-Lite exhibits 25% better ITR and has reduced memory requirements by 92% and single-target identification cycle time by 26%.

Fast generation of covariance matrices for weak lensing

Upcoming weak lensing surveys will probe large fractions of the sky with unprecedented accuracy. To infer cosmological constraints, a large ensemble of survey simulations are required to accurately model cosmological observables and their covariances. We develop a parallelized multi-lens-plane pipeline called UFALCON, designed to generate full-sky weak lensing maps from lightcones within a minimal runtime. It makes use of L-PICOLA (Howlett et al. [1]), an approximate numerical code, which provides a fast and accurate alternative to cosmological N-Body simulations. The UFALCON maps are constructed by nesting 2 simulations with mass resolution of about 5 × 1012 and 2 × 1013 h−1 M⊙ covering a redshift-range from z=0.1 to 1.5 without replicating the simulation volume. We compute the convergence and projected overdensity maps for L-PICOLA in the lightcone or snapshot mode. The generation of such a map, including the L-PICOLA simulation, takes about 3 hours walltime on 220 cores. We use the maps to calculate the spherical harmonic power spectra, which we compare to theoretical predictions and to UFALCON results generated using the full N-Body code GADGET-2. We then compute the covariance matrix of the full-sky spherical harmonic power spectra using 150 UFALCON maps based on L-PICOLA in lightcone mode. We consider the PDF, the higher-order moments and the variance of the smoothed field variance to quantify the accuracy of the covariance matrix, which we find to be a few percent for scales ℓ ∼ 102 to 103. We test the impact of this level of accuracy on cosmological constraints using an optimistic survey configuration, and find that the final results are robust to this level of uncertainty. The speed and accuracy of our developed pipeline provides a basis to also include further important features such as masking, varying noise and will allow us to compute covariance matrices for models beyond ΛCDM.

Noise Robust Speaker Recognition Based on Adaptive Frame Weighting in GMM for i-Vector Extraction

Even though speaker recognition has gained significant progress in recent years, its performance is known to be deteriorated severely with the existence of strong background noises. Inspired by a recently proposed clean-frame selection approach, this work investigates a relatively elegant weighting method when computing the Baum-Welch statistics of Gaussian mixture models (GMMs) in i-vector extraction. By introducing weighting parameters to the frames of enrollment/testing utterances, the optimization problem is redefined and solved. New updating rules are derived by incorporating weights to the computation of posterior probabilities, mean vectors, and covariance matrices of the GMM. The experiments conducted on the Speakers in the Wild (SITW) database show that the proposed algorithm has significantly improved the performance of i-vector-based speaker recognition systems in noisy environments. Compared with the GMM i-vector baseline, the equal error rate is reduced from 5.75 to 4.72 and the minimum value of cost function (C det min ) is reduced from 0.4825 to 0.4505. Slight but significant superiority is also observed over the method with an additional feature enhancement frontend by using deep neural networks.

Principal Component Analysis as a Dimensionality Reduction and Data Preprocessing Technique

Nowadays, dealing with high dimension data has become common in many fields such as network security, image processing, medical diagnosis, biometric systems, e-commerce, etc. In data base with higher dimension the direct use of data is costlier in terms of its storage, processing, mathematical computations etc. Moreover, in many applications with wireless networks, Received Signal Strength (RSS) needs to be processed to remove the redundant readings. In this paper, we discussed Principal Component Analysis (PCA) as a dimensionality reduction technique. PCA can be done either by calculating the covariance matrix or by Singular Value Decomposition (SVD). We used covariance matrix calculation due to its less complexity. Simulation results verify that the correlated input data sequence is sorted to uncorrelated principal components (PC’s) with decreasing variation and some of first PC’s can represent nearly all data sets.

Weld Bead Detection Based on 3D Geometric Features and Machine Learning Approaches

Weld bead detection is essential for automated welding inspection processes. The non-invasive passive techniques, such as photogrammetry, are quickly evolving to provide a 3D point cloud with submillimeter precision and spatial resolution. However, its application in weld visual inspection has not been extensively studied. The derived 3D point clouds, despite the lack of topological information, store significant information for the weld-plaque segmentation. Although the weld bead detection is being carried out over images or based on laser profiles, its characterization by means of 3D geometrical features has not been assessed. Moreover, it is possible to combine machine learning approaches and the 3D features in order to realize the full potential of the weld bead segmentation of 3D submillimeter point clouds. In this paper, the novelty is focused on the study of 3D features on real cases to identify the most relevant ones for weld bead detection on the basis of the information gain. For this novel contribution, the influence of neighborhood size for covariance matrix computation, decision tree algorithms, and split criteria are analyzed to assess the optimal results. The classification accuracy is evaluated by the degree of agreement of the classified data by the kappa index and the area under the receiver operating characteristic (ROC) curve. The experimental results show that the proposed novel methodology performs better than 0.85 for the kappa index and better than 0.95 for ROC area.

Revealing quantum mechanical effects in enzyme catalysis with large-scale electronic structure simulation.

Enzymes have evolved to facilitate challenging reactions at ambient conditions with specificity seldom matched by other catalysts. Computational modeling provides valuable insight into catalytic mechanism, and the large size of enzymes mandates multi-scale, quantum mechanical-molecular mechanical (QM/MM) simulations. Although QM/MM plays an essential role in balancing simulation cost to enable sampling with full QM treatment needed to understand electronic structure in enzyme active sites, the relative importance of these two strategies for understanding enzyme mechanism is not well known. We explore challenges in QM/MM for studying the reactivity and stability of three diverse enzymes: i) Mg2+-dependent catechol O-methyltransferase (COMT), ii) radical enzyme choline trimethylamine lyase (CutC), and iii) DNA methyltransferase (DNMT1), which has structural Zn2+ binding sites. In COMT, strong non-covalent interactions lead to long range coupling of electronic structure properties across the active site, but the more isolated nature of the metallocofactor in DNMT1 leads to faster convergence of some properties. We quantify these effects in COMT by computing covariance matrices of by-residue electronic structure properties during dynamics and along the reaction coordinate. In CutC, we observe spontaneous bond cleavage following initiation events, highlighting the importance of sampling and dynamics. We use electronic structure analysis to quantify the relative importance of CHO and OHO non-covalent interactions in imparting reactivity. These three diverse cases enable us to provide some general recommendations regarding QM/MM simulation of enzymes.

3D cosmic shear: Numerical challenges, 3D lensing random fields generation, and Minkowski functionals for cosmological inference

Cosmic shear - the weak gravitational lensing effect generated by fluctuations of the gravitational tidal fields of the large-scale structure - is one of the most promising tools for current and future cosmological analyses. The spherical-Bessel decomposition of the cosmic shear field ("3D cosmic shear") is one way to maximise the amount of redshift information in a lensing analysis and therefore provides a powerful tool to investigate in particular the growth of cosmic structure that is crucial for dark energy studies. However, the computation of simulated 3D cosmic shear covariance matrices presents numerical difficulties, due to the required integrations over highly oscillatory functions. We present and compare two numerical methods and relative implementations to perform these integrations. We then show how to generate 3D Gaussian random fields on the sky in spherical coordinates, starting from the 3D cosmic shear covariances. To validate our field-generation procedure, we calculate the Minkowski functionals associated with our random fields, compare them with the known expectation values for the Gaussian case and demonstrate parameter inference from Minkowski functionals from a cosmic shear survey. This is a first step towards producing fully 3D Minkowski functionals for a lognormal field in 3D to extract Gaussian and non-Gaussian information from the cosmic shear field, as well as towards the use of Minkowski functionals as a probe of cosmology beyond the commonly used two-point statistics.

Covariances of galaxy stellar mass functions and correlation functions

We compute covariance matrices for many observed estimates of the stellar mass function of galaxies from $z=0$ to $z\approx 4$, and for one estimate of the projected correlation function of galaxies split by stellar mass at $z\lesssim 0.5$. All covariance matrices include contributions due to large scale structure, the preference for galaxies to be found in groups and clusters, and for shot noise. These covariance matrices are made available for use in constraining models of galaxy formation and the galaxy-halo connection.