Design of low rank estimators for higher-order statistics based on the second-order statistics

2003 ◽  
Author(s):  
I. Bradaric ◽  
A.P. Petropulu
Keyword(s):  
Order Statistics ◽  
Higher Order ◽  
Second Order ◽  
Low Rank ◽  
Higher Order Statistics ◽  
Second Order Statistics

Low-rank estimation of higher order statistics

1997 ◽  
Vol 45 (3) ◽  
pp. 673-685 ◽  
Author(s):  
T.F. Andre ◽  
R.D. Nowak ◽  
B.D. Van Veen
Keyword(s):  
Order Statistics ◽  
Higher Order ◽  
Low Rank ◽  
Higher Order Statistics ◽  
Rank Estimation

Spatial nonlinearities in the instantaneous perception of textures with identical power spectra

1980 ◽  
Vol 290 (1038) ◽  
pp. 83-94 ◽  
Keyword(s):  
Order Statistics ◽  
Power Spectra ◽  
Building Blocks ◽  
Second Order ◽  
Perceptual System ◽  
Higher Order Statistics ◽  
Line Segments ◽  
Second Order Statistics ◽  
Local Structures ◽  
Perception System

In 1962, Julesz observed that texture pairs with identical second-order statistics but different third- and higher-order statistics were usually not discriminable without scrutiny. Since second-order (dipole) statistics determine the autocorrelation functions and hence the power spectra, this observation also meant that in preattentive perception of texture the phase (position) spectra were ignored. In the last two decades many new classes of texture pairs with identical power spectra have been invented that were not effortlessly discriminable; however, recently (Caelli & Julesz 1978; Caelli et al . 1978; Julesz et al . 1978) several counterexamples were found. In these texture pairs with identical power spectra some local structures of ‘quasi-collinearity’, ‘corner’, ‘closure’ and ‘granularity’ yielded strong discrimination. These features can be regarded as the fundamental building blocks of form, that is, the essential nonlinearities of the preattentive perceptual system. Here, it will be shown that these counterexamples are not independent of each other, but can be described by two elementary units: bars (line segments) and their terminators. Furthermore, the preattentive texture perception system can count the number of terminators but ignores their positions.

scholarly journals Colour of turbulence

2017 ◽  
Vol 812 ◽  
pp. 636-680 ◽  
Author(s):  
Armin Zare ◽  
Mihailo R. Jovanović ◽  
Tryphon T. Georgiou
Keyword(s):  
Order Statistics ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
Complex Dynamics ◽  
Second Order ◽  
Low Rank ◽  
Navier Stokes ◽  
Mean Velocity ◽  
Navier Stokes Equations ◽  
Second Order Statistics

In this paper, we address the problem of how to account for second-order statistics of turbulent flows using low-complexity stochastic dynamical models based on the linearized Navier–Stokes equations. The complexity is quantified by the number of degrees of freedom in the linearized evolution model that are directly influenced by stochastic excitation sources. For the case where only a subset of velocity correlations are known, we develop a framework to complete unavailable second-order statistics in a way that is consistent with linearization around turbulent mean velocity. In general, white-in-time stochastic forcing is not sufficient to explain turbulent flow statistics. We develop models for coloured-in-time forcing using a maximum entropy formulation together with a regularization that serves as a proxy for rank minimization. We show that coloured-in-time excitation of the Navier–Stokes equations can also be interpreted as a low-rank modification to the generator of the linearized dynamics. Our method provides a data-driven refinement of models that originate from first principles and captures complex dynamics of turbulent flows in a way that is tractable for analysis, optimization and control design.

Propagating Skewness and Kurtosis Through Engineering Models for Low-Cost, Meaningful, Nondeterministic Design

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Travis V. Anderson ◽  
Christopher A. Mattson
Keyword(s):  
Order Statistics ◽  
Taylor Series ◽  
Computational Cost ◽  
Higher Order ◽  
Second Order ◽  
System Model ◽  
Higher Order Statistics ◽  
Actual System ◽  
System Output ◽  
Skewness And Kurtosis

System models help designers predict actual system output. Generally, variation in system inputs creates variation in system outputs. Designers often propagate variance through a system model by taking a derivative-based weighted sum of each input’s variance. This method is based on a Taylor-series expansion. Having an output mean and variance, designers typically assume the outputs are Gaussian. This paper demonstrates that outputs are rarely Gaussian for nonlinear functions, even with Gaussian inputs. This paper also presents a solution for system designers to more meaningfully describe the system output distribution. This solution consists of using equations derived from a second-order Taylor series that propagate skewness and kurtosis through a system model. If a second-order Taylor series is used to propagate variance, these higher-order statistics can also be propagated with minimal additional computational cost. These higher-order statistics allow the system designer to more accurately describe the distribution of possible outputs. The benefits of including higher-order statistics in error propagation are clearly illustrated in the example of a flat-rolling metalworking process used to manufacture metal plates.

Higher order versus second order statistics in ultrasound image deconvolution

1997 ◽  
Vol 44 (6) ◽  
pp. 1409-1416 ◽  
Author(s):  
U.R. Abeyratne ◽  
A.P. Petropulu ◽  
J.M. Reid ◽  
T. Golas ◽  
E. Conant ◽  
...  
Keyword(s):  
Order Statistics ◽  
Ultrasound Image ◽  
Higher Order ◽  
Second Order ◽  
Image Deconvolution ◽  
Second Order Statistics
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