3D signal reconstruction from noisy projection data for stochastic objects as a generalization of Gaussian mixture parameter estimation

2010 ◽  
Author(s):  
Yili Zheng ◽  
Peter C. Doerschuk
Keyword(s):  
Parameter Estimation ◽  
Signal Reconstruction ◽  
Gaussian Mixture ◽  
Projection Data ◽  
Mixture Parameter ◽  
Noisy Projection

Rainfall-Rate Estimation Using Gaussian Mixture Parameter Estimator: Training and Validation

2012 ◽  
Vol 29 (5) ◽  
pp. 731-744 ◽  
Author(s):  
Zhengzheng Li ◽  
Yan Zhang ◽  
Scott E. Giangrande
Keyword(s):  
General Framework ◽  
Gaussian Mixture ◽  
Minimum Variance ◽  
Rainfall Rate ◽  
Polarimetric Radar ◽  
Parameter Estimator ◽  
Minimum Variance Unbiased Estimator ◽  
Rate Estimation ◽  
Parameter Estimations ◽  
Mixture Parameter

Abstract This study develops a Gaussian mixture rainfall-rate estimator (GMRE) for polarimetric radar-based rainfall-rate estimation, following a general framework based on the Gaussian mixture model and Bayes least squares estimation for weather radar–based parameter estimations. The advantages of GMRE are 1) it is a minimum variance unbiased estimator; 2) it is a general estimator applicable to different rain regimes in different regions; and 3) it is flexible and may incorporate/exclude different polarimetric radar variables as inputs. This paper also discusses training the GMRE and the sensitivity of performance to mixture number. A large radar and surface gauge observation dataset collected in central Oklahoma during the multiyear Joint Polarization Experiment (JPOLE) field campaign is used to evaluate the GMRE approach. Results indicate that the GMRE approach can outperform existing polarimetric rainfall techniques optimized for this JPOLE dataset in terms of bias and root-mean-square error.

scholarly journals Regularized Parameter Estimation in High-Dimensional Gaussian Mixture Models

2011 ◽  
Vol 23 (6) ◽  
pp. 1605-1622 ◽  
Author(s):  
Lingyan Ruan ◽  
Ming Yuan ◽  
Hui Zou
Keyword(s):  
Parameter Estimation ◽  
Mixture Models ◽  
Gaussian Mixture Models ◽  
Expectation Maximization Algorithm ◽  
Real Data ◽  
Gaussian Mixture ◽  
High Dimensional ◽  
Model Based Clustering ◽  
Text Type ◽  
Effective Dimensionality

Finite gaussian mixture models are widely used in statistics thanks to their great flexibility. However, parameter estimation for gaussian mixture models with high dimensionality can be challenging because of the large number of parameters that need to be estimated. In this letter, we propose a penalized likelihood estimator to address this difficulty. The [Formula: see text]-type penalty we impose on the inverse covariance matrices encourages sparsity on its entries and therefore helps to reduce the effective dimensionality of the problem. We show that the proposed estimate can be efficiently computed using an expectation-maximization algorithm. To illustrate the practical merits of the proposed method, we consider its applications in model-based clustering and mixture discriminant analysis. Numerical experiments with both simulated and real data show that the new method is a valuable tool for high-dimensional data analysis.

scholarly journals GPU-based fast cone beam CT reconstruction from undersampled and noisy projection data via total variation

2010 ◽  
Vol 37 (4) ◽  
pp. 1757-1760 ◽  
Author(s):  
Xun Jia ◽  
Yifei Lou ◽  
Ruijiang Li ◽  
William Y. Song ◽  
Steve B. Jiang
Keyword(s):  
Total Variation ◽  
Cone Beam Ct ◽  
Cone Beam ◽  
Projection Data ◽  
Ct Reconstruction ◽  
Noisy Projection

scholarly journals Segmentation of Remotely Sensed Images using Unsupervised ‘Sampling-Resampling’ based on Hopfield Type Neural Network

2018 ◽  
Vol 7 (02) ◽  
pp. 23606-23612
Author(s):  
R. Cheryal Percy
Keyword(s):  
Neural Network ◽  
Parameter Estimation ◽  
Neural Network Model ◽  
Bayesian Learning ◽  
Satellite Images ◽  
Gaussian Mixture Models ◽  
Gaussian Mixture ◽  
Integration Technique ◽  
Unsupervised Segmentation ◽  
Practical Applications

In this paper we propose a technique for performing unsupervised segmentation for satellite images using a ’sampling – resampling’ based on Hopfield type Neural Network. The multi band values of the satellite images are grouped into clusters that are modeled using Gaussians. The parameters of Gaussian mixture models are learnt using Hopfield Type Neural Network. The purpose of this work is to show the effectiveness of the results obtained by using Hopfield type Neural Network rather than Bayesian parameter estimation. Each spatial position in the considered image is represented by neuron that is connected only to its neighboring units. It can be observed that the proposed technique have a better correspondence to the actual land features in the satellite images than compared with the results obtained by using the clustering technique like K-means Algorithm.  The unsupervised techniques learns the class parameter by exploiting the structure of the unlabeled data .However ,the numerical integration technique that are required for implementing Bayesian learning becomes complicated for practical applications, because of involving large data’s than compared to the Hopfield type Neural Network model.

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