scholarly journals Providing a New Approach for Modeling and Parameter Estimation of Probability Density Function of Noise in Digital Images

2015 ◽  
Vol 37 ◽  
pp. 182
Author(s):  
Hanif Yaghoobi ◽  
Keivan Maghooli ◽  
Alireza Ghahramani Barandagh
Keyword(s):  
Parameter Estimation ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Digital Images ◽  
Image Sensors ◽  
Arrival Process ◽  
Mean And Variance ◽  
Two Parameters ◽  
Generalized Probability

The main part of the noise in digital images arises when taking pictures or transmission. There is noise in the imagescaptured by the image sensors of the real world. Noise, based on its causes can have different probability density functions.For example, such a model is called the Poisson distribution function of the random nature of photon arrival process that isconsistent with the distribution of pixel values measured. The parameters of the noise probability density function (PDF)can be achieved to some extent the properties of the sensor. But, we need to estimate the parameters for imaging settings. Ifwe assume that the PDF of noise is approximately Gaussian, then we need only to estimate the mean and variance becausethe Gaussian PDF with only two parameters is determined. In fact, in many cases, PDF of noise is not Gaussian and it hasunknown distribution. In this study, we introduce a generalized probability density function for modeling noise in imagesand propose a method to estimate its parameters. Because the generalized probability density function has multipleparameters, so use common parameter estimation techniques such as derivative method to maximize the likelihood functionwould be extremely difficult. In this study, we propose the use of evolutionary algorithms for global optimization. Theresults show that this method accurately estimates the probability density function parameters.

scholarly journals A particle-filter framework for robust cryoEM 3D reconstruction

2018 ◽  
Author(s):  
Mingxu Hu ◽  
Hongkun Yu ◽  
Kai Gu ◽  
Kunpeng Wang ◽  
Siyuan Ren ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Probability Density Function ◽  
Particle Filter ◽  
Probability Density ◽  
Density Function ◽  
Sequential Monte Carlo ◽  
High Dimensional ◽  
Dimensional Parameter ◽  
Support Points ◽  
Estimated Parameters

AbstractElectron cryo-microscopy (cryoEM) is now a powerful tool in determining atomic structures of biological macromolecules under nearly natural conditions. The major task of single-particle cryoEM is to estimate a set of parameters for each input particle image to reconstruct the three-dimensional structure of the macromolecules. As future large-scale applications require increasingly higher resolution and automation, robust high-dimensional parameter estimation algorithms need to be developed in the presence of various image qualities. In this paper, we introduced a particle-filter algorithm for cryoEM, which was a sequential Monte Carlo method for robust and fast high-dimensional parameter estimation. The cryoEM parameter estimation problem was described by a probability density function of the estimated parameters. The particle filter uses a set of random and weighted support points to represent such a probability density function. The statistical properties of the support points not only enhance the parameter estimation with self-adaptive accuracy but also provide the belief of estimated parameters, which is essential for the reconstruction phase. The implementation of these features showed strong tolerance to bad particles and enabled robust defocus refinement, demonstrated by the remarkable resolution improvement at the atomic level.

Mechanical Error Analysis of Spatial Linkages

1978 ◽  
Vol 100 (4) ◽  
pp. 732-738 ◽  
Author(s):  
S. G. Dhande ◽  
J. Chakraborty
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Experimental Information ◽  
Output Error ◽  
Revolute Joints ◽  
Analysis And Synthesis ◽  
Mean And Variance ◽  
Synthesis Procedure ◽  
Spatial Linkages

In this paper the effect on the output error of function-generating spatial linkages due to tolerances on the links and clearances at the hinges is analyzed. Tolerances on link lengths are assumed to be normally distributed. For the clearance error in spherical, prismatic, and revolute joints, uniform probability density function is assumed. However, the models developed and the analysis procedure proposed can be used for any other probability density function including the mean and variance values derived from experimental information. A synthesis procedure to allocate tolerances and clearances on different members of linkages to restrict the output error within specified units is developed. Results of analysis and synthesis are given for two example problems involving RRSS and RSSR mechanisms.

scholarly journals Improved Chebyshev inequality: new probability bounds with known supremum of PDF

2018 ◽  
Author(s):  
Tomohiro Nishiyama
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Probability Distributions ◽  
Chebyshev Inequality ◽  
Discrete Probability ◽  
One Dimensional ◽  
Probability Bounds ◽  
Mean And Variance ◽  
Discrete Probability Distributions

In this paper, we derive new probability bounds for Chebyshev's inequality if the supremum of the probability density function is known.This result holds for one-dimensional or multivariate continuous probability distributions with finite mean and variance (covariance matrix).We also show that the similar result holds for specific discrete probability distributions.

Scalar probability density function and fine structure in uniformly sheared turbulence

2002 ◽  
Vol 461 ◽  
pp. 155-182 ◽  
Author(s):  
M. FERCHICHI ◽  
S. TAVOULARIS
Keyword(s):  
Fine Structure ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Conditional Expectations ◽  
Scalar Variance ◽  
Self Similar ◽  
Variance Equation ◽  
Non Gaussian ◽  
Two Parameters

This study is an experimental investigation of the probability density function (p.d.f.) and the fine structure of temperature fluctuations in uniformly sheared turbulence with a passively introduced uniform mean temperature gradient. The shear parameter was relatively large, resulting in vigorous turbulence production and a total mean strain up to 23. The turbulence Reynolds number was up to 253. The scalar fluctuations grew in a self-similar fashion and at the same exponential rate as the turbulence stresses, in conformity with predictions based on an analytical solution of the scalar variance equation. Analytical considerations as well as measurements demonstrate that the scalar p.d.f. is essentially Gaussian and that the scalar–velocity joint p.d.f. is essentially jointly Gaussian, with the conditional expectations of the velocity fluctuations linearly dependent on the scalar value. Joint statistics of the scalar and its dissipation rate indicate a statistical independence of the two parameters. The fine structure of the scalar was invoked from statistics of derivatives and differences of the scalar, in both the streamwise and transverse directions. Probability density functions of scalar derivatives and differences in the dissipative and the inertial ranges were strongly non-Gaussian and skewed, displaying flared, asymmetric tails. All measurements point to a highly intermittent scalar fine structure, even more intermittent than the fine structure of the turbulent velocity.

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