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- Aurélia Fraysse, Béatrice Pesquet-Popescu, Jean-Christophe Pesquet
- IEEE Transactions on Information Theory
- 2009

We consider the uniform scalar quantization of a class of mixed distributed memoryless sources, namely sources having a Bernoulli Generalized Gaussian (BGG) distribution. Both for low and high resolutions, asymptotic expressions of the distortion for a pth-order moment error measure, and close approximations of the entropy are provided for these sources.… (More)

- Aurelia Fraysse, Thomas Rodet
- 2011 IEEE Statistical Signal Processing Workshop…
- 2011

In this paper we provide a new algorithm allowing to solve a variational Bayesian issue which can be seen as a functional optimization problem. The main contribution of this paper is to transpose a classical iterative algorithm of optimization in the metric space of probability densities involved in the Bayesian methodology. Another important part is the… (More)

- Aurélia Fraysse, Thomas Rodet
- SIAM J. Imaging Sciences
- 2014

In this paper we provide an algorithm allowing to solve the variational Bayesian issue as a functional optimization problem. The main contribution of this paper is to transpose a classical iterative algorithm of optimization in the metric space of probability densities involved in the Bayesian methodology. The main advantage of this methodology is that it… (More)

- Yuling Zheng, Aurélia Fraysse, Thomas Rodet
- IEEE Transactions on Image Processing
- 2015

Variational Bayesian approximations have been widely used in fully Bayesian inference for approximating an intractable posterior distribution by a separable one. Nevertheless, the classical variational Bayesian approximation (VBA) method suffers from slow convergence to the approximate solution when tackling large dimensional problems. To address this… (More)

- Aurélia Fraysse, Béatrice Pesquet-Popescu, Jean-Christophe Pesquet
- 2008 IEEE International Conference on Acoustics…
- 2008

In this paper, we provide operational rate-distortion results for memoryless generalized Gaussian sources. Close approximations of the entropy are provided for these sources, after a uniform scalar quantization at low/high resolution. Asymptotic expressions of the distortion for an arbitrary p-th order error measure are also given. The resulting… (More)

- Mounir Kaaniche, Aurélia Fraysse, Béatrice Pesquet-Popescu, Jean-Christophe Pesquet
- IEEE Transactions on Image Processing
- 2014

In this paper, we develop an efficient bit allocation strategy for subband-based image coding systems. More specifically, our objective is to design a new optimization algorithm based on a rate-distortion optimality criterion. To this end, we consider the uniform scalar quantization of a class of mixed distributed sources following a Bernoulli-generalized… (More)

- Mounir Kaaniche, Aurélia Fraysse, Béatrice Pesquet-Popescu, Jean-Christophe Pesquet
- 2014 IEEE International Conference on Acoustics…
- 2014

The objective of this paper is to study rate-distortion properties of a quantized Bernoulli-Generalized Gaussian source. Such source model has been found to be well-adapted for signals having a sparse representation in a transformed domain. We provide here accurate approximations of the entropy and the distortion functions evaluated through a p-th order… (More)

The objective of this paper is to design an efficient bit allocation algorithm in the subband coding context based on an analytical approach. More precisely, we consider the uniform scalar quantization of subband coefficients modeled by a Generalized Gaussian distribution. This model appears to be particularly well-adapted for data having a sparse… (More)

- A. Fraysse
- 2009

In nonparametric statistics an optimality criterion for estimation procedures is provided by the minimax rate of convergence. However this classical point of view is subject to controversy as it requires to look for the worst behaviour reached by an estimation procedure in a given space. The purpose of this paper is to show that this is not justified as the… (More)

Our aim is to solve a linear inverse problem using various methods based on the Variational Bayesian Approximation (VBA). We choose to take sparsity into account via a scale mixture prior, more precisely a student-t model. The joint posterior of the unknown and hidden variable of the mixtures is approximated via the VBA. To do this approximation,… (More)