38 research outputs found
A Hierarchical Bayesian Model for Frame Representation
In many signal processing problems, it may be fruitful to represent the
signal under study in a frame. If a probabilistic approach is adopted, it
becomes then necessary to estimate the hyper-parameters characterizing the
probability distribution of the frame coefficients. This problem is difficult
since in general the frame synthesis operator is not bijective. Consequently,
the frame coefficients are not directly observable. This paper introduces a
hierarchical Bayesian model for frame representation. The posterior
distribution of the frame coefficients and model hyper-parameters is derived.
Hybrid Markov Chain Monte Carlo algorithms are subsequently proposed to sample
from this posterior distribution. The generated samples are then exploited to
estimate the hyper-parameters and the frame coefficients of the target signal.
Validation experiments show that the proposed algorithms provide an accurate
estimation of the frame coefficients and hyper-parameters. Application to
practical problems of image denoising show the impact of the resulting Bayesian
estimation on the recovered signal quality
A comparison of soft and hard decision-directed feedforward phase estimators
Publication in the conference proceedings of EUSIPCO, Florence, Italy, 200
Exponential families of mixed Poisson distributions
If I=(I1,…,Id) is a random variable on [0,∞)d with distribution μ(dλ1,…,dλd), the mixed Poisson distribution MP(μ) on View the MathML source is the distribution of (N1(I1),…,Nd(Id)) where N1,…,Nd are ordinary independent Poisson processes which are also independent of I. The paper proves that if F is a natural exponential family on [0,∞)d then MP(F) is also a natural exponential family if and only if a generating probability of F is the distribution of v0+v1Y1+cdots, three dots, centered+vqYq for some qless-than-or-equals, slantd, for some vectors v0,…,vq of [0,∞)d with disjoint supports and for independent standard real gamma random variables Y1,…,Yq
Study and simulation of parametric model output probability laws
A finite linear combination ofIndependent Identically Distributed (i. i.d) non Gaussian
variables cannot be Gaussian. In the case of an infinite linear combination,
the Gaussian assumption is often considered by applying the limit central theorem .
The output ofARMA (possibly AR) filters is an infinite sum of independent input
samples . The aim of this paper is to study the output law of these filters and more
precisely its « tendency » to the Gaussian law.Une combinaison linéaire finie de variables aléatoires independantes de même loi non gaussienne ne peut être gaussienne. Dans le cas d'une combinaison linéaire infinie, il est d'usage de conclure à la normalité par application systématique du théorème de la limite centrale. La sortie des filtres Autorégressifs (AR) ou Autorégressifs à Moyenne Ajustée (ARMA) s'exprime sous la forme d'une somme infinie d'échantillons de l'entrée du modèle. Nous étudions dans cet article la loi de la sortie de ces filtres et plus particulièrement leur «proximite» avec la loi gaussienn
MCMC Algorithms for Supervised and Unsupervised Linear Unmixing of Hyperspectral Images
This book is a collection of 19 articles which reflect the courses given at the Collège de France/Summer school “Reconstruction d'images − Applications astrophysiques“ held in Nice and Fréjus, France, from June 18 to 22, 2012. The articles presented in this volume address emerging concepts and methods that are useful in the complex process of improving our knowledge of the celestial objects, including Earth
Analyse statistique de la détection de planètes par imagerie directe
- Cette communication est consacrée à la détection de planètes par imagerie directe. L'accent est mis sur les deux facteurs dégradants : les résidus de turbulence atmosphérique et la présence du coronographe. Une modélisation statistique des mesures permet de proposer et d'étudier un détecteur utilisant des images à court temps de pose. Une simulation numérique met en évidence le gain de cette technique par rapport à une image long temps de pose ou au traitement courte pose habituel
Unsupervised Bayesian linear unmixing of gene expression microarrays
Background: This paper introduces a new constrained model and the corresponding algorithm, called unsupervised Bayesian linear unmixing (uBLU), to identify biological signatures from high dimensional assays like gene expression microarrays. The basis for uBLU is a Bayesian model for the data samples which are represented as an additive mixture of random positive gene signatures, called factors, with random positive mixing coefficients, called factor scores, that specify the relative contribution of each signature to a specific sample. The particularity of the proposed method is that uBLU constrains the factor loadings to be non-negative and the factor scores to be probability distributions over the factors. Furthermore, it also provides estimates of the number of factors. A Gibbs sampling strategy is adopted here to generate random samples according to the posterior distribution of the factors, factor scores, and number of factors. These samples are then used to estimate all the unknown parameters. Results: Firstly, the proposed uBLU method is applied to several simulated datasets with known ground truth and compared with previous factor decomposition methods, such as principal component analysis (PCA), non negative matrix factorization (NMF), Bayesian factor regression modeling (BFRM), and the gradient-based algorithm for general matrix factorization (GB-GMF). Secondly, we illustrate the application of uBLU on a real time-evolving gene expression dataset from a recent viral challenge study in which individuals have been inoculated with influenza A/H3N2/Wisconsin. We show that the uBLU method significantly outperforms the other methods on the simulated and real data sets considered here. Conclusions: The results obtained on synthetic and real data illustrate the accuracy of the proposed uBLU method when compared to other factor decomposition methods from the literature (PCA, NMF, BFRM, and GB-GMF). The uBLU method identifies an inflammatory component closely associated with clinical symptom scores collected during the study. Using a constrained model allows recovery of all the inflammatory genes in a single factor
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
Vacuum configurations for renormalizable non-commutative scalar models
In this paper we find non-trivial vacuum states for the renormalizable
non-commutative model. An associated linear sigma model is then
considered. We further investigate the corresponding spontaneous symmetry
breaking.Comment: 17 page
Subsystem dynamics under random Hamiltonian evolution
We study time evolution of a subsystem's density matrix under unitary
evolution, generated by a sufficiently complex, say quantum chaotic,
Hamiltonian, modeled by a random matrix. We exactly calculate all coherences,
purity and fluctuations. We show that the reduced density matrix can be
described in terms of a noncentral correlated Wishart ensemble for which we are
able to perform analytical calculations of the eigenvalue density. Our
description accounts for a transition from an arbitrary initial state towards a
random state at large times, enabling us to determine the convergence time
after which random states are reached. We identify and describe a number of
other interesting features, like a series of collisions between the largest
eigenvalue and the bulk, accompanied by a phase transition in its distribution
function.Comment: 16 pages, 8 figures; v3: slightly re-structured and an additional
appendi