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.

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.

Adaptive Interacting Multiple Model Unscented Particle Filter Tracking Algorithm

2012 ◽  
Vol 190-191 ◽  
pp. 906-910 ◽  
Author(s):  
Hong Jiang Liu
Keyword(s):  
Probability Density Function ◽  
Particle Filter ◽  
Probability Density ◽  
Real Time ◽  
Density Function ◽  
Tracking System ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
Tracking Accuracy ◽  
Unscented Particle Filter

In order to study the tracking problem of maneuvering image sequence target in complex environment with multi-sensor array, the adaptive interacting multiple model unscented particle filter algorithm based on measured residual is proposed. The motion array tracking system dynamic model is established, and initialized probability density function also is defined based on unscented transformation, after that, the measured covariance and state covariance are online adjusted by measured residual and adaptive factor, then the self-adapting capability of filter gain and the real-time capability of posterior probability density function are improved. Finally, the simulation results between different algorithms show the validity and superiority of the presented algorithm in tracking accuracy, stability and real-time capability.

Adaptive Interacting Multiple Model Unscented Particle Filter for Dynamic Acoustic Array

2013 ◽  
Vol 300-301 ◽  
pp. 407-413
Author(s):  
Ya Lei Liu ◽  
Xiao Hui Gu
Keyword(s):  
Probability Density Function ◽  
Particle Filter ◽  
Probability Density ◽  
Real Time ◽  
Density Function ◽  
Interacting Multiple Model ◽  
Multiple Model ◽  
Tracking Accuracy ◽  
Unscented Particle Filter ◽  
Acoustic Array

Abstract. In order to improve the tracking accuracy of 3D dynamic acoustic array to 2D maneuvering target in colored noise environment, the adaptive interacting multiple model unscented particle filter algorithm based on measured residual is proposed. The 3D motion acoustic array tracking system dynamic model is established, and initialized probability density function also is defined based on unscented transformation, after that, the measured covariance and state covariance are online adjusted by measured residual and adaptive factor, then the self-adapting capability of filter gain and the real-time capability of posterior probability density function are improved. Finally, the simulation results between different algorithms show the validity and superiority of the presented algorithm in tracking accuracy, stability and real-time capability.

On the Use of the Posterior Crame´r-Rao Lower Bound for Damage Estimation in Structural Health Management

2009 ◽  
Author(s):  
Jun Jason Zhang ◽  
Wenfan Zhou ◽  
Narayan Kovvali ◽  
Antonia Papandreou-Suppappola ◽  
Aditi Chattopadhyay
Keyword(s):  
Probability Density Function ◽  
Lower Bound ◽  
Probability Density ◽  
Density Function ◽  
Sequential Monte Carlo ◽  
Likelihood Function ◽  
Transition Probability ◽  
Estimation Error ◽  
Stochastic Dynamic ◽  
Transition Probability Density

The use of the posterior Crame´r-Rao lower bound (PCRLB) as a lower bound for the mean-squared estimation error (MSEE) of progressive damage is investigated. The estimation problem is formulated in terms of a stochastic dynamic system model that describes the random evolution of damage and provides measurement uncertainty. Based on whether the system is linear or nonlinear, sequential Monte Carlo techniques are used to approximate the posterior probability density function and thus obtain the damage state estimate. The resulting MSEE is compared to the lower bound offered by the PCRLB that is obtained from the implied state transition probability density function and the measurement likelihood function. The progressive estimation results and the PCRLB are demonstrated for fatigue crack estimation in an aluminum compact-tension (CT) sample subjected to variable-amplitude loading.

Seismic attribute selection for machine-learning-based facies analysis

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. O17-O35
Author(s):  
Jie Qi ◽  
Bo Zhang ◽  
Bin Lyu ◽  
Kurt Marfurt
Keyword(s):  
Machine Learning ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Facies Analysis ◽  
Attribute Selection ◽  
Seismic Facies ◽  
High Dimensional ◽  
Karst Collapse ◽  
Optimum Number

Interpreters face two main challenges in seismic facies analysis. The first challenge is to define, or “label,” the facies of interest. The second challenge is to select a suite of attributes that can differentiate a target facies from the background reflectivity. Our key objective is to determine which seismic attributes can best differentiate one class of chaotic seismic facies from another using modern machine-learning technology. Although simple 1D histograms provide a list of candidate attributes, they do not provide insight into the optimum number or combination of attributes. To address this limitation, we have conducted an exhaustive search whereby we represent the target and background training facies by high-dimensional Gaussian mixture models (GMMs) for each potential attribute combination. The first step is to choose candidate attributes that may be able to differentiate chaotic mass-transport deposits and salt diapirs from the more conformal, coherent background reflectors. The second step is to draw polygons around the target and background facies to provide the labeled data to be represented by GMMs. Maximizing the distance between all GMM facies pairs provides the optimum number and combination of attributes. We use generative topographic mapping to represent the high-dimensional attribute data by a lower dimensional 2D manifold. Each labeled facies provides a probability density function on the manifold that can be compared to the probability density function of each voxel, providing the likelihood that a given voxel is a member of each of the facies. Our first example maps chaotic seismic facies associated with the development of salt diapirs and minibasins. Our second example successfully delineates karst collapse underlying a shale resource play from north Texas.

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