Coherence-based Partial Exact Recovery Condition for OMP/OLS

We address the exact recovery of the support of a k-sparse vector with Orthogonal Matching Pursuit (OMP) and Orthogonal Least Squares (OLS) in a noiseless setting. We consider the scenario where OMP/OLS have selected good atoms during the first l iterations (l<k) and derive a new sufficient and worst-case necessary condition for their success in k steps. Our result is based on the coherence \mu of the dictionary and relaxes Tropp's well-known condition \mu<1/(2k-1) to the case where OMP/OLS have a partial knowledge of the support

Estimation régularisée et non supervisée de la réponse hémodynamique en imagerie cérébrale fonctionnelle (IRMf)

L'estimation de la fonction de réponse hémodynamique (FRH) en imagerie par résonance magnétique fonctionnelle (IRMf) est essentielle pour une meilleure compréhension des activations cérébrales. Nous abordons ce problème dans un cadre bayésien en introduisant un a priori temporel sur la FRH et sous une forme non supervisée en maximisant la log-vraisemblance vis-à-vis des hyperparamètres. L'originalité de ce travail réside dans la définition d'une nouvelle fonction de vraisemblance, au nombre de paramètres réduit, qui vise d'une part à améliorer la prise en compte de la variabilité des artefacts physiologiques (coeur, respiration), et d'autre part à accélérer la convergence de l'algorithme EM utilisé pour la maximiser. Nous montrons l'intérêt de cette approche en la comparant aux travaux pré-existants [1], à la fois en simulation et sur données réelles

Imagerie des milieux stratifies: modelisation markovienne, application a la deconvolution sismique

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : T 78378 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Bayesian Approach to Inverse Problems

Many scientific, medical or engineering problems raise the issue of recovering some physical quantities from indirect measurements; for instance, detecting or quantifying flaws or cracks within a material from acoustic or electromagnetic measurements at its surface is an essential problem of non-destructive evaluation. The concept of inverse problems precisely originates from the idea of inverting the laws of physics to recover a quantity of interest from measurable data.Unfortunately, most inverse problems are ill-posed, which means that precise and stable solutions are not easy to devise. Regularization is the key concept to solve inverse problems.The goal of this book is to deal with inverse problems and regularized solutions using the Bayesian statistical tools, with a particular view to signal and image estimatio

Fast MCMC Computations for the Estimation of Sparse Processes from Noisy Observations

This paper presents a fast MCMC algorithm specially designed for high dimensional models with block structure. Such models are often met in Bayesian inference, such as spectral estimation, harmonic analysis, blind deconvolution or signal classication. Our algorithm generates samples distributed according to a posterior distribution. We show that sampling the amplitudes together with the remaining model parameters leads to quicker computations than sampling from the marginal posterior, where amplitudes have been integrated out. Simulation results demonstrate the soundness of this approach for high dimensional models

Števniki in števila v Homerjevi Odiseji : študijsko gradivo : zgodovina matematike

Števnike in števila srečujemo tudi v svetovni književnosti. V gradivu bomo predstavili tiste, ki jih je Homer uporabil v svoji Odiseji. Števila v pesnitvi niso nič posebnega, večina je namreč takih, ki jih še dandanes uporabljamo v vsakdanjih pogovorih in katerih velikost je običajnim ljudem zlahka pred- stavljiva