85,979 research outputs found
Bayesian separation of spectral sources under non-negativity and full additivity constraints
This paper addresses the problem of separating spectral sources which are
linearly mixed with unknown proportions. The main difficulty of the problem is
to ensure the full additivity (sum-to-one) of the mixing coefficients and
non-negativity of sources and mixing coefficients. A Bayesian estimation
approach based on Gamma priors was recently proposed to handle the
non-negativity constraints in a linear mixture model. However, incorporating
the full additivity constraint requires further developments. This paper
studies a new hierarchical Bayesian model appropriate to the non-negativity and
sum-to-one constraints associated to the regressors and regression coefficients
of linear mixtures. The estimation of the unknown parameters of this model is
performed using samples generated using an appropriate Gibbs sampler. The
performance of the proposed algorithm is evaluated through simulation results
conducted on synthetic mixture models. The proposed approach is also applied to
the processing of multicomponent chemical mixtures resulting from Raman
spectroscopy.Comment: v4: minor grammatical changes; Signal Processing, 200
Sparse Estimation using Bayesian Hierarchical Prior Modeling for Real and Complex Linear Models
In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been
used to model sparsity-inducing priors that realize a class of concave penalty
functions for the regression task in real-valued signal models. Motivated by
the relative scarcity of formal tools for SBL in complex-valued models, this
paper proposes a GSM model - the Bessel K model - that induces concave penalty
functions for the estimation of complex sparse signals. The properties of the
Bessel K model are analyzed when it is applied to Type I and Type II
estimation. This analysis reveals that, by tuning the parameters of the mixing
pdf different penalty functions are invoked depending on the estimation type
used, the value of the noise variance, and whether real or complex signals are
estimated. Using the Bessel K model, we derive a sparse estimator based on a
modification of the expectation-maximization algorithm formulated for Type II
estimation. The estimator includes as a special instance the algorithms
proposed by Tipping and Faul [1] and by Babacan et al. [2]. Numerical results
show the superiority of the proposed estimator over these state-of-the-art
estimators in terms of convergence speed, sparseness, reconstruction error, and
robustness in low and medium signal-to-noise ratio regimes.Comment: The paper provides a new comprehensive analysis of the theoretical
foundations of the proposed estimators. Minor modification of the titl
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