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Variational Bayes Group Sparse Time-Adaptive Parameter Estimation With Either Known or Unknown Sparsity Pattern

 

Authors: K. E. Themelis, A. A. Rontogiannis, K. D. Koutroumbas
Journal: IEEE Transactions on Signal Processing
Year: 2016
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Abstract

In this paper, we study the problem of time-adaptive group sparse signal estimation from a Bayesian viewpoint. We propose two online variational Bayes schemes that are specifically designed to estimate and track group sparse signals in time. The proposed schemes address both the cases where the grouping information of the signal is either known or not. For the case of known group sparsity pattern, the proposed scheme builds on a novel hierarchical model for the Bayesian adaptive group lasso. Utilizing the variational Bayes framework, update equations for all model parameters are given, for both the batch and time adaptive estimation scenarios. To address the case where the group sparsity pattern is unknown, the hierarchical Bayesian model of the former scheme is extended by organizing the penalty parameters of the Bayesian lasso in a conditional autoregressive model. Intrinsic conditional autoregression is exploited to penalize the signal coefficients in a structured manner and thus obtain group sparse solutions automatically. Again, a robust and computationally efficient online variational Bayes estimator is developed, capitalizing on the conjugacy of the proposed hierarchical Bayesian formulation. Experimental results are reported that corroborate the superior estimation performance of the proposed online schemes, when compared with state-of-the-art methods.

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Simultaneously sparse and low-rank abundance matrix estimation for hyperspectral image unmixing

 

Authors: P. V. Giampouras, K. E. Themelis, A. A. Rontogiannis, K. D. Koutroumbas
Journal: IEEE Transactions on Geoscience and Remote Sensing
Year: 2016
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Abstract

In a plethora of applications dealing with inverse problems, e.g., image processing, social networks, compressive sensing, and biological data processing, the signal of interest is known to be structured in several ways at the same time. This premise has recently guided research into the innovative and meaningful idea of imposing multiple constraints on the unknown parameters involved in the problem under study. For instance, when dealing with problems whose unknown parameters form sparse and low-rank matrices, the adoption of suitably combined constraints imposing sparsity and low rankness is expected to yield substantially enhanced estimation results. In this paper, we address the spectral unmixing problem in hyperspectral images. Specifically, two novel unmixing algorithms are introduced in an attempt to exploit both spatial correlation and sparse representation of pixels lying in the homogeneous regions of hyperspectral images. To this end, a novel mixed penalty term is first defined consisting of the sum of the weighted ℓ1 and the weighted nuclear norm of the abundance matrix corresponding to a small area of the image determined by a sliding square window. This penalty term is then used to regularize a conventional quadratic cost function and impose simultaneous sparsity and low rankness on the abundance matrix. The resulting regularized cost function is minimized by: 1) an incremental proximal sparse and low-rank unmixing algorithm; and 2) an algorithm based on the alternating direction method of multipliers. The effectiveness of the proposed algorithms is illustrated in experiments conducted both on simulated and real data.

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A Variational Bayes Framework for Sparse Adaptive Estimation

 

Authors: K. E. Themelis, A. A. Rontogiannis, K. D. Koutroumbas
Journal: IEEE Transactions on Signal Processing
Year: 2014
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Abstract

Recently, a number of mostly l1-norm regularized least-squares-type deterministic algorithms have been proposed to address the problem of sparse adaptive signal estimation and system identification. From a Bayesian perspective, this task is equivalent to maximum a posteriori probability estimation under a sparsity promoting heavy-tailed prior for the parameters of interest. Following a different approach, this paper develops a unifying framework of sparse variational Bayes algorithms that employ heavy-tailed priors in conjugate hierarchical form to facilitate posterior inference. The resulting fully automated variational schemes are first presented in a batch iterative form. Then, it is shown that by properly exploiting the structure of the batch estimation task, new sparse adaptive variational Bayes algorithms can be derived, which have the ability to impose and track sparsity during real-time processing in a time-varying environment. The most important feature of the proposed algorithms is that they completely eliminate the need for computationally costly parameter fine-tuning, a necessary ingredient of sparse adaptive deterministic algorithms. Extensive simulation results are provided to demonstrate the effectiveness of the new sparse adaptive variational Bayes algorithms against state-of-the-art deterministic techniques for adaptive channel estimation. The results show that the proposed algorithms are numerically robust and exhibit in general superior estimation performance compared to their deterministic counterparts..

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On the Unmixing of MeX/OMEGA Hyperspectral Data

 

Authors: K. E. Themelis, F. Schmidt, O. Sykioti, A. A. Rontogiannis, K. D. Koutroumbas, I. A. Daglis
Journal: Planetary and Space Science
Year: 2012
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Abstract

This paper presents a comparative study of three different types of estimators used for supervised linear unmixing of two MEx/OMEGA hyperspectral cubes. The algorithms take into account the constraints of the abundance fractions, in order to get physically interpretable results. Abundance maps show that the Bayesian maximum a posteriori probability (MAP) estimator proposed in Themelis and Rontogiannis (2008) outperforms the other two schemes, offering a compromise between complexity and estimation performance. Thus, the MAP estimator is a candidate algorithm to perform ice and minerals detection on large hyperspectral datasets.

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A Novel Hierarchical Bayesian Approach for Sparse Semi-Supervised Hyperspectral Unmixing

 

Authors: K. E. Themelis, A. A. Rontogiannis, K. D. Koutroumbas
Journal: IEEE Transactions on Signal Processing
Year: 2012
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Abstract

In this paper the problem of semisupervised hyperspectral unmixing is considered. More specifically, the unmixing process is formulated as a linear regression problem, where the abundance’s physical constraints are taken into account. Based on this formulation, a novel hierarchical Bayesian model is proposed and suitable priors are selected for the model parameters such that, on the one hand, they ensure the nonnegativity of the abundances, while on the other hand they favor sparse solutions for the abundances’ vector. Performing Bayesian inference based on the proposed hierarchical Bayesian model, a new low-complexity iterative method is derived, and its connection with Gibbs sampling and variational Bayesian inference is highlighted. Experimental results on both synthetic and real hyperspectral data illustrate that the proposed method converges fast, favors sparsity in the abundances’ vector, and offers improved estimation accuracy compared to other related methods.