Convex Parameter Estimation of Perturbed Multivariate Generalized Gaussian Distributions

The multivariate generalized Gaussian distribution (MGGD), also known as the multivariate exponential power (MEP) distribution, is widely used in signal and image processing. However, estimating MGGD parameters, which is required in practical applications, still faces specific theoretical challenges...

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Vydané v:IEEE transactions on signal processing Ročník 72; s. 4132 - 4146
Hlavní autori: Ouzir, Nora, Pascal, Frederic, Pesquet, Jean-Christophe
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York IEEE 01.01.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Predmet:
Computer Science
Convergence
convex optimization
Convexity
Cost analysis
Cost function
Covariance matrices
Covariance matrix
Estimation
Gaussian distribution
Image processing
Machine Learning
Mathematics
Methodology
Multivariate analysis
multivariate exponential power distributions
multivariate generalized Gaussian distribution
Normal distribution
Optimization
Optimization and Control
Parameter estimation
Perturbation
Perturbation methods
precision matrix
Regularization
robust estimation
Robustness
Signal and Image Processing
Statistics
Symmetric matrices
Vectors
Multivariate Generalized Gaussian Distribution
Convex Optimization
Robust Estimation
Elliptically Contoured Distributions
Multivariate Exponential Power Distributions
Precision Matrix Estimation
ISSN:1053-587X, 1941-0476
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Popis
Shrnutí:The multivariate generalized Gaussian distribution (MGGD), also known as the multivariate exponential power (MEP) distribution, is widely used in signal and image processing. However, estimating MGGD parameters, which is required in practical applications, still faces specific theoretical challenges. In particular, establishing convergence properties for the standard fixed-point approach when both the distribution mean and the scatter (or the precision) matrix are unknown is still an open problem. In robust estimation, imposing classical constraints on the precision matrix, such as sparsity, has been limited by the non-convexity of the resulting cost function. This paper tackles these issues from an optimization viewpoint by proposing a convex formulation with well-established convergence properties. We embed our analysis in a noisy scenario where robustness is induced by modelling multiplicative perturbations. The resulting framework is flexible as it combines a variety of regularizations for the precision matrix, the mean and model perturbations. This paper presents proof of the desired theoretical properties, specifies the conditions preserving these properties for different regularization choices and designs a general proximal primal-dual optimization strategy. The experiments show a more accurate precision and covariance matrix estimation with similar performance for the mean vector parameter compared to Tyler's <inline-formula><tex-math notation="LaTeX">M</tex-math></inline-formula>-estimator. In a high-dimensional setting, the proposed method outperforms the classical GLASSO, one of its robust extensions, and the regularized Tyler's estimator.
Bibliografia:ObjectType-Article-1
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2024.3453509