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A New Riemannian Averaged Fixed-Point Algorithm for MGGD Parameter Estimation

Zois Boukouvalas, Salem Said, Lionel Bombrun, Yannick Berthoumieu, Tulay Adali
2015 IEEE Signal Processing Letters  
Since many applications require flexible estimation of the shape parameter, we propose a new FP algorithm, Riemannian averaged FP (RA-FP), which can effectively estimate the scatter matrix for any value  ...  Existing fixed-point (FP) algorithms provide an easy to implement method for estimating the scatter matrix, but are known to fail, giving highly inaccurate results, when the value of the shape parameter  ...  CONCLUSION This paper presented a new FP algorithm, for the estimation of MGGD parameters, Σ, β and m.  ... 
doi:10.1109/lsp.2015.2478803 fatcat:dmi7mmock5gzpjuqlo5ffizhwa

Online estimation of MGGD: the Riemannian Averaged Natural Gradient method

Jialun Zhou, Salem Said, Yannick Berthoumieu
2019 2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)  
To overcome this difficulty, the present paper proposes a new method for online estimation of MGGD parameters, called the Riemannian Averaged Natural Gradient (RANG) method.  ...  Unfortunately, estimating the parameters of MGGD leads to non-linear matrix equations, whose solution becomes unpractical in high-dimensional problems, or when dealing with very large datasets.  ...  To deal with this issue, the present paper introduces a new method for online estimation of the parameters of MGGD.  ... 
doi:10.1109/camsap45676.2019.9022517 dblp:conf/camsap/ZhouSB19 fatcat:dfp2dk5wfzhudobw4wumvoqaci

Riemannian information gradient methods for the parameter estimation of ECD: Some applications in image processing [article]

Jialun Zhou, Salem Said, Yannick Berthoumieu
2020 arXiv   pre-print
Maximum likelihood. estimation (MLE) of ECD leads to a system of non-linear equations, most-often addressed using fixed-point (FP) methods.  ...  To develop the ISG method, the Riemannian information gradient is derived taking into account the product manifold associated to the underlying parameter space of the ECD.  ...  Acknowledgement At the end, we thank the support from the ANR MAR-GARITA under Grant ANR-17-ASTR-0015 for our works.  ... 
arXiv:2011.02806v1 fatcat:y4e2wcyx7vgglmozntkdwqc3ii

Development of ICA and IVA Algorithms with Application to Medical Image Analysis [article]

Zois Boukouvalas
2018 arXiv   pre-print
In this work, we first introduce a flexible ICA algorithm that uses an effective PDF estimator to accurately capture the underlying statistical properties of the data.  ...  We then discuss several techniques to accurately estimate the parameters of the multivariate generalized Gaussian distribution, and how to integrate them into the IVA model.  ...  - Develop a new and efficient ML estimation technique based on the Fisher scoring (FS) that estimates both the shape parameter and the scatter matrix; -Develop a new fixed point (FP) algorithm, called  ... 
arXiv:1801.08600v1 fatcat:nu2xlytexrcnnblws7zieo77be

Multivariate Generalized Gaussian Distribution: Convexity and Graphical Models

Teng Zhang, Ami Wiesel, Maria Sabrina Greco
2013 IEEE Transactions on Signal Processing  
Our second contribution is a generalized framework for structured covariance estimation under sparsity constraints.  ...  Our first contribution is a new analysis of this likelihood based on geodesic convexity that requires weaker assumptions.  ...  In Section III we provide a new geodesic analysis of MGGD estimation, and in Section IV we introduce a convex optimization framework for chordal structured MGGD estimation.  ... 
doi:10.1109/tsp.2013.2267740 fatcat:i6yzyjfprbgl5lf44vkwwmos7i