Texture classification with cross-covariance matrices in compressive measurement domain

2016 ◽  
Vol 10 (8) ◽  
pp. 1377-1384 ◽  
Author(s):  
Jie Guo ◽  
Bin Song ◽  
Fang Tian ◽  
Hao Qin
Keyword(s):  
Texture Classification ◽  
Covariance Matrices ◽  
Measurement Domain ◽  
Cross Covariance

scholarly journals Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space

2020 ◽  
Vol 497 (2) ◽  
pp. 1684-1711 ◽  
Author(s):  
Naonori S Sugiyama ◽  
Shun Saito ◽  
Florian Beutler ◽  
Hee-Jong Seo
Keyword(s):  
Perturbation Theory ◽  
Power Spectrum ◽  
Shot Noise ◽  
Signal To Noise Ratio ◽  
Covariance Matrices ◽  
Theory Approach ◽  
Cross Covariance ◽  
The Galaxy ◽  
The Cross ◽  
Non Gaussian

ABSTRACT In this paper, we predict the covariance matrices of both the power spectrum and the bispectrum, including full non-Gaussian contributions, redshift space distortions, linear bias effects, and shot-noise corrections, using perturbation theory (PT). To quantify the redshift-space distortion effect, we focus mainly on the monopole and quadrupole components of both the power and bispectra. We, for the first time, compute the 5- and 6-point spectra to predict the cross-covariance between the power and bispectra, and the autocovariance of the bispectrum in redshift space. We test the validity of our calculations by comparing them with the covariance matrices measured from the MultiDark-Patchy mock catalogues that are designed to reproduce the galaxy clustering measured from the Baryon Oscillation Spectroscopic Survey Data Release 12. We argue that the simple, leading-order PT works because the shot-noise corrections for the Patchy mocks are more dominant than other higher order terms we ignore. In the meantime, we confirm some discrepancies in the comparison, especially of the cross-covariance. We discuss potential sources of such discrepancies. We also show that our PT model reproduces well the cumulative signal-to-noise ratio of the power spectrum and the bispectrum as a function of maximum wavenumber, implying that our PT model captures successfully essential contributions to the covariance matrices.

ENCODING STRUCTURAL SIMILARITY BY CROSS-COVARIANCE TENSORS FOR IMAGE CLASSIFICATION

2014 ◽  
Vol 28 (07) ◽  
pp. 1460008
Author(s):  
MARCO SAN BIAGIO ◽  
SAMUELE MARTELLI ◽  
MARCO CROCCO ◽  
MARCO CRISTANI ◽  
VITTORIO MURINO
Keyword(s):  
Computer Vision ◽  
Covariance Matrix ◽  
Image Representation ◽  
Structural Similarity ◽  
Covariance Matrices ◽  
Integral Image ◽  
Computational Burden ◽  
Feature Vectors ◽  
Single Region ◽  
Cross Covariance

In computer vision, an object can be modeled in two main ways: by explicitly measuring its characteristics in terms of feature vectors, and by capturing the relations which link an object with some exemplars, that is, in terms of similarities. In this paper, we propose a new similarity-based descriptor, dubbed structural similarity cross-covariance tensor (SS-CCT), where self-similarities come into play: Here the entity to be measured and the exemplar are regions of the same object, and their similarities are encoded in terms of cross-covariance matrices. These matrices are computed from a set of low-level feature vectors extracted from pairs of regions that cover the entire image. SS-CCT shares some similarities with the widely used covariance matrix descriptor, but extends its power focusing on structural similarities across multiple parts of an image, instead of capturing local similarities in a single region. The effectiveness of SS-CCT is tested on many diverse classification scenarios, considering objects and scenes on widely known benchmarks (Caltech-101, Caltech-256, PASCAL VOC 2007 and SenseCam). In all the cases, the results obtained demonstrate the superiority of our new descriptor against diverse competitors. Furthermore, we also reported an analysis on the reduced computational burden achieved by using and efficient implementation that takes advantage from the integral image representation.

Simulation of fine-scale electrical conductivity fields using resolution-limited tomograms and area-to-point kriging

2019 ◽  
Vol 218 (2) ◽  
pp. 1322-1335 ◽  
Author(s):  
Raphaël Nussbaumer ◽  
Niklas Linde ◽  
Grégoire Mariethoz ◽  
Klaus Holliger
Keyword(s):  
Electrical Conductivity ◽  
Large Scale ◽  
Synthetic Data ◽  
Linear Mapping ◽  
Covariance Matrices ◽  
Fine Scale ◽  
Geostatistical Model ◽  
Tomographic Images ◽  
Monte Carlo Techniques ◽  
Cross Covariance

SUMMARY Deterministic geophysical inversion approaches yield tomographic images with strong imprints of the regularization terms required to solve otherwise ill-posed inverse problems. While such tomograms enable an adequate assessment of the larger-scale features of the probed subsurface, the finer-scale details tend to be unresolved. Yet, representing these fine-scale structural details is generally desirable and for some applications even mandatory. To address this problem, we have developed a two-step methodology based on area-to-point kriging to generate fine-scale multi-Gaussian realizations from smooth tomographic images. Specifically, we use a co-kriging system in which the smooth, low-resolution tomogram is related to the fine-scale heterogeneity through a linear mapping operation. This mapping is based on the model resolution and the posterior covariance matrices computed using a linearization around the final tomographic model. This, in turn, allows us for analytical computations of covariance and cross-covariance models. The methodology is tested on a heterogeneous synthetic 2-D distribution of electrical conductivity that is probed with a surface-based electrical resistivity tomography (ERT) survey. The results demonstrate the ability of this technique to reproduce a known geostatistical model characterizing the fine-scale structure, while simultaneously preserving the large-scale structures identified by the smoothness-constrained tomographic inversion. Small discrepancies between the geophysical forward responses of the realizations and the reference synthetic data are attributed to the underlying linearization. Overall, the method provides an effective and fast alternative to more comprehensive, but computationally more expensive approaches, such as, for example, Markov chain Monte Carlo techniques. Moreover, the proposed method can be used to generate fine-scale multivariate Gaussian realizations from virtually any smoothness-constrained inversion results given the corresponding resolution and posterior covariance matrices.

scholarly journals A partition-enhanced least-squares collocation approach (PE-LSC)

2021 ◽  
Vol 95 (8) ◽  
Author(s):  
P. Zingerle ◽  
R. Pail ◽  
M. Willberg ◽  
M. Scheinert
Keyword(s):  
Least Squares ◽  
Computational Cost ◽  
Computation Time ◽  
Covariance Matrices ◽  
Kernel Functions ◽  
Intermediate Step ◽  
Target Area ◽  
Least Squares Collocation ◽  
Isotropic Coordinates ◽  
Cross Covariance

AbstractWe present a partition-enhanced least-squares collocation (PE-LSC) which comprises several modifications to the classical LSC method. It is our goal to circumvent various problems of the practical application of LSC. While these investigations are focused on the modeling of the exterior gravity field the elaborated methods can also be used in other applications. One of the main drawbacks and current limitations of LSC is its high computational cost which grows cubically with the number of observation points. A common way to mitigate this problem is to tile the target area into sub-regions and solve each tile individually. This procedure assumes a certain locality of the LSC kernel functions which is generally not given and, therefore, results in fringe effects. To avoid this, it is proposed to localize the LSC kernels such that locality is preserved, and the estimated variances are not notably increased in comparison with the classical LSC method. Using global covariance models involves the calculation of a large number of Legendre polynomials which is usually a time-consuming task. Hence, to accelerate the creation of the covariance matrices, as an intermediate step we pre-calculate the covariance function on a two-dimensional grid of isotropic coordinates. Based on this grid, and under the assumption that the covariances are sufficiently smooth, the final covariance matrices are then obtained by a simple and fast interpolation algorithm. Applying the generalized multi-variate chain rule, also cross-covariance matrices among arbitrary linear spherical harmonic functionals can be obtained by this technique. Together with some further minor alterations these modifications are implemented in the PE-LSC method. The new PE-LSC is tested using selected data sets in Antarctica where altogether more than 800,000 observations are available for processing. In this case, PE-LSC yields a speed-up of computation time by a factor of about 55 (i.e., the computation needs only hours instead of weeks) in comparison with the classical unpartitioned LSC. Likewise, the memory requirement is reduced by a factor of about 360 (i.e., allocating memory in the order of GB instead of TB).

scholarly journals Multimodal Sensor Selection for Multiple Spatial Field Reconstruction

2021 ◽  
Author(s):  
Linh Nguyen ◽  
Karthick Thiyagarajan ◽  
Nalika Ulapane ◽  
sarath kodagoda
Keyword(s):  
Random Fields ◽  
Real Life ◽  
Covariance Matrices ◽  
Sensor Selection ◽  
Sensor Nodes ◽  
Approximate Algorithm ◽  
Selection Problem ◽  
Cross Covariance ◽  
Efficient Prediction ◽  
Selection For

The paper addresses the multimodal sensor selection problem where selected collocated sensor nodes are employed to effectively monitor and efficiently predict multiple spatial random fields. It is first proposed to exploit multivariate Gaussian processes (MGP) to model multiple spatial phenomena jointly. By the use of the Matern cross-covariance function, cross covariance matrices in the MGP model are sufficiently positive semi-definite, concomitantly providing efficient prediction of all multivariate processes at unmeasured locations. The multimodal sensor selection problem is then formulated and solved by an approximate algorithm with an aim to select the most informative sensor nodes so that prediction uncertainties at all the fields are minimized. The proposed approach was validated in the real-life experiments with promising results.

scholarly journals Distributed Fusion Estimation for Multisensor Multirate Systems with Stochastic Observation Multiplicative Noises

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Peng Fangfang ◽  
Sun Shuli
Keyword(s):  
Computational Cost ◽  
Covariance Matrices ◽  
The State ◽  
Multirate Systems ◽  
Multiplicative Noises ◽  
Cross Covariance ◽  
Sampling Points ◽  
Optimal Fusion ◽  
The Cross ◽  
Local Filters

This paper studies the fusion estimation problem of a class of multisensor multirate systems with observation multiplicative noises. The dynamic system is sampled uniformly. Sampling period of each sensor is uniform and the integer multiple of the state update period. Moreover, different sensors have the different sampling rates and observations of sensors are subject to the stochastic uncertainties of multiplicative noises. At first, local filters at the observation sampling points are obtained based on the observations of each sensor. Further, local estimators at the state update points are obtained by predictions of local filters at the observation sampling points. They have the reduced computational cost and a good real-time property. Then, the cross-covariance matrices between any two local estimators are derived at the state update points. At last, using the matrix weighted optimal fusion estimation algorithm in the linear minimum variance sense, the distributed optimal fusion estimator is obtained based on the local estimators and the cross-covariance matrices. An example shows the effectiveness of the proposed algorithms.

scholarly journals Multivariate versus Univariate Sensor Selection for Spatial Field Estimation

2021 ◽  
Author(s):  
Linh Nguyen
Keyword(s):  
Random Fields ◽  
Covariance Function ◽  
Covariance Matrices ◽  
Sensor Selection ◽  
Spatial Processes ◽  
Selection Problems ◽  
Cross Covariance ◽  
Field Estimation ◽  
Spatial Fields ◽  
Selection For

<pre>The paper discusses the sensor selection problem in estimating spatial fields. It is demonstrated that selecting a subset of sensors depends on modelling spatial processes. It is first proposed to exploit Gaussian process (GP) to model a univariate spatial field and multivariate GP (MGP) to jointly represent multivariate spatial phenomena. A Mat\'ern cross-covariance function is employed in the MGP model to guarantee its cross-covariance matrices to be positive semi-definite. We then consider two corresponding \textit{univariate} and \textit{multivariate sensor selection} problems in effectively monitoring multiple spatial random fields. The sensor selection approaches were implemented in the real-world experiments and their performances were compared. Difference of results obtained by the univariate and multivariate sensor selection techniques is insignificant; that is, either of the methods can be efficiently used in practice.</pre>

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