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This article deals with an extension of the split gradient method (SGM) applied to the optimization of any divergence between two data fields, under positivity and flux conservation constraints. SGM is guaranteed to converge for convex cost functions. A SGM-based algorithm is also derived to solve the nonnegative matrix factorization (NMF) problem. It is(More)
Dynamic system modeling plays a crucial role in the development of techniques for stationary and non-stationary signal processing. Due to the inherent physical characteristics of systems usually under investigation, non-negativity is a desired constraint that can be imposed on the parameters to estimate. In this paper, we propose a general method for system(More)
Spectral unmixing is an important issue to analyze remotely sensed hyperspectral data. This involves the decomposition of each mixed pixel into its pure endmember spectra, and the estimation of the abundance value for each endmember. Although linear mixture models are often considered because of their simplicity, there are many situations in which they can(More)
In hyperspectral image analysis, pixels are mixtures of spectral components associated to pure materials. Although the linear mixture model is the mostly studied case, nonlinear techniques have been proposed to overcome its limitations. In this paper, a manifold learning approach is used as a dimensionality-reduction step to deal with non-linearities(More)
This paper addresses the problem of linear unmixing for hyperspectral imagery. This problem can be formulated as a linear regression problem whose regression coefficients (abundances) satisfy sum-toone and positivity constraints. Two scaled gradient iterative methods are proposed for estimating the abundances of the linear mixing model. The first method is(More)
The aim of this paper is Bayesian estimation of the parameters of a polynomial phase signal. This problem , encountered i n r adar systems for example, is usually solved using a time-frequency analysis or phase-only algorithms, see [4] for a detailed introduction. A Bayesian approach using Markov chain Monte Carlo (MCMC) methods for estimating a posteriori(More)
We consider the problem of restoring astronomical images acquired with charge coupled device cameras. The astronomical object is first blurred by the point spread function of the instrument-atmosphere set. The resulting convolved image is corrupted by a Poissonian noise due to low light intensity, then, a Gaussian white noise is added during the electronic(More)
We use reversible jump Markov c hain Monte Carlo MCMC methods to address the problem of order and parameters estimation of noisy polynomial-phase signals within a Bayesian framework. As posterior distributions of the parameters are not tractable, MCMC methods are used to simulate them. EEcient model jumping is achieved by proposing model space moves from(More)
This article deals with a regularized version of the split gradient method (SGM), leading to multiplicative algorithms. The proposed algorithm is available for the optimization of any divergence depending on two data fields under positivity constraint. The SGM-based algorithm is derived to solve the nonnegative matrix factorization (NMF) problem. An example(More)