scholarly journals The Maximum Entropy on the Mean Method for Image Deblurring

2020 ◽  
Author(s):  
Gabriel Rioux ◽  
Rustum Choksi ◽  
Tim Hoheisel ◽  
Pierre Marechal ◽  
Christopher Scarvelis
Keyword(s):  
Maximum Entropy ◽  
Image Deblurring ◽  
The Mean

Uncertainty Quantification of Energy Harvesting Systems Using Method of Quadratures and Maximum Entropy Principle

2015 ◽  
Author(s):  
Aditya Nanda ◽  
M. Amin Karami ◽  
Puneet Singla
Keyword(s):  
Energy Harvesting ◽  
Maximum Entropy ◽  
Density Function ◽  
Root Mean Square ◽  
Maximum Entropy Principle ◽  
Mean Square ◽  
Mean Power ◽  
Harvesting Systems ◽  
Entropy Principle ◽  
The Mean

This paper uses the method of Quadratures in conjunction with the Maximum Entropy principle to investigate the effect of parametric uncertainties on the mean power output and root mean square deflection of piezoelectric vibrational energy harvesting systems. Uncertainty in parameters of harvesters could arise from insufficient manufacturing controls or change in material properties over time. We investigate bimorph based harvesters that transduce ambient vibrations to electricity via the piezoelectric effect. Three varieties of energy harvesters — Linear, Nonlinear monostable and Nonlinear bistable are considered in this research. This analysis quantitatively shows the probability density function for the mean power and root mean square deflection as a function of the probability densities of the excitation frequency, excitation amplitude, initial deflection of the bimorph and magnet gap of the energy harvester. The method of Quadratures is used for numerically integrating functions by propagating weighted points from the domain and evaluating the integral as a weighted sum of the function values. In this paper, the method of Quadratures is used for evaluating central moments of the distributions of rms deflection and mean harvested power and, then, in conjunction with the principle of Maximum Entropy (MaxEnt) an optimal density function is obtained which maximizes the entropy and satisfies the moment constraints. The The computed nonlinear density functions are validated against Monte Carlo simulations thereby demonstrating the efficiency of the approach. Further, the Maximum Entropy principle is widely applicable to uncertainty quantification of a wide range of dynamic systems.

scholarly journals Functional calibration estimation by the maximum entropy on the mean principle

Statistics ◽  
2014 ◽  
Vol 49 (5) ◽  
pp. 989-1004 ◽  
Author(s):  
S. Gallón ◽  
F. Gamboa ◽  
J.M. Loubes
Keyword(s):  
Maximum Entropy ◽  
The Mean

scholarly journals Two new preconditioners for mean curvature-based image deblurring problem

2021 ◽  
Vol 6 (12) ◽  
pp. 13824-13844
Author(s):  
Shahbaz Ahmad ◽  
◽  
Adel M. Al-Mahdi ◽  
Rashad Ahmed ◽  
◽  
...  
Keyword(s):  
Mean Curvature ◽  
Krylov Subspace ◽  
Numerical Algorithms ◽  
Image Deblurring ◽  
Krylov Subspace Methods ◽  
Positive Definite ◽  
Lagrange Equations ◽  
Symmetric Positive Definite ◽  
The Mean

<abstract><p>The mean curvature-based image deblurring model is widely used to enhance the quality of the deblurred images. However, the discretization of the associated Euler-Lagrange equations produce a nonlinear ill-conditioned system which affect the convergence of the numerical algorithms like Krylov subspace methods. To overcome this difficulty, in this paper, we present two new symmetric positive definite (SPD) preconditioners. An efficient algorithm is presented for the mean curvature-based image deblurring problem which combines a fixed point iteration (FPI) with new preconditioned matrices to handle the nonlinearity and ill-conditioned nature of the large system. The eigenvalues analysis is also presented in the paper. Fast convergence has shown in the numerical results by using the proposed new preconditioners.</p></abstract>

scholarly journals On the Long-Period Variations in the Rate of the Earth's Rotation

1979 ◽  
Vol 82 ◽  
pp. 59-60
Author(s):  
A. I. Emetz ◽  
A. A. Korsun'
Keyword(s):  
Power Spectrum ◽  
Maximum Entropy ◽  
Rotational Speed ◽  
Monthly Data ◽  
Long Period ◽  
Period Variations ◽  
Similar Series ◽  
The Mean ◽  
Using Data ◽  
Linear Trends

The maximum entropy power spectrum (Smylie, et al., 1974) of the Earth's rotational speed was calculated using data from 1900 to 1976. Two series of data were analyzed. The first was a series of δω/ω) determined from annual UT1 - ET data from 1900 to 1976. The second was a similar series derived from the mean monthly data of UT1 - TAI. Linear trends were removed from both series before analysis. Using the second series of data, significant periods of 2.8, 3.7, 7.0, and 10.5 years were found. The first series showed significant periods at 6, 10, 13, 22, and 57 years. Of these periodicities those at 22 and 57 years showed the largest amplitudes (0.454 ± 0.097 × 10−8 and 1.431 ± 0.104 × 10−8 respectively).

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