Patrick Héas

• http://people.rennes.inria.fr/Patrick.Heas
• Researcher at INRIA Center of Rennes

This paper deals with the estimation of rare event probabilities using importance sampling (IS), where an optimal proposal distribution is computed with the cross-entropy (CE) method. Although, IS optimized with the CE method leads to an efficient reduction of the estimator variance, this approach remains unaffordable for problems where the repeate...

This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach can be formalised as attempting to solve a low-rank constrained optimisation problem. This problem is non-convex and state-of-the-art algorithms are all sub-optimal....

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation by first embedding the trajectories in a reproducing kernel Hilbert space (RKHS), which exhibits appealing ap...

This paper deals with model order reduction of parametrical dynamical systems. We consider the specific setup where the distribution of the system's trajectories is unknown but the following two sources of information are available: \textit{(i)} some "rough" prior knowledge on the system's realisations; \textit{(ii)} a set of "incomplete" observati...

This paper deals with model-order reduction of parametric partial differential equations (PPDE). More specifically, we consider the problem of finding a good approximation subspace of the solution manifold of the PPDE when only partial information on the latter is available. We assume that two sources of information are available: i) a “rough” prio...

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation by first embedding the trajectories in a reproducing kernel Hilbert space (RKHS), which has interesting appro...

This work proposes an adaptive sequential Monte Carlo sampling algorithm for solving inverse Bayesian problems in a context where a (costly) likelihood evaluation can be approximated by a surrogate, constructed from previous evaluations of the true likelihood. A rough error estimation of the obtained surrogates is required. The method is based on a...

Atmospheric motion vectors (AMVs) extracted from satellite imagery are the only wind observations with good global coverage. They are important features for feeding numerical weather prediction (NWP) models. Several Bayesian models have been proposed to estimate AMVs. Although critical for correct assimilation into NWP models, very few methods prov...

In this work, we present an efficient optic flow algorithm for the extraction of vertically resolved 3D atmospheric motion vector (AMV) fields from incomplete hyperspectral image data measures by infrared sounders. The model at the heart of the energy to be minimized is consistent with atmospheric dynamics, incorporating ingredients of thermodynamics,...

In this work, we present an efficient optic flow algorithm for the extraction of vertically resolved 3D atmospheric motion vector (AMV) fields from incomplete hyperspectral image data measures by infrared sounders. The model at the heart of the energy to be minimized is consistent with atmospheric dynamics, incorporating ingredients of thermodynami...

Importance sampling of target probability distributions belonging to a given convex class is considered. Motivated by previous results, the cost of importance sampling is quantified using the relative entropy of the target with respect to proposal distributions. Using a reference measure as a reference for cost, we prove under some general conditio...

Atmospheric motion vectors (AMVs) extracted from satellite imagery are the only wind observations with good global coverage. They are important features for feeding numerical weather prediction (NWP) models. Several Bayesian models have been proposed to estimate AMVs. Although critical for correct assimilation into NWP models, very few methods prov...

This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition. Searching this approximation in a data-driven approach is formalized as attempting to solve a low-rank constrained optimization problem. This problem is non-convex, and state-of-the-art algorithms are all sub-optimal. This pap...

This technical note reviews sate-of-the-art algorithms for linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). While repeating several parts of our article "low-rank dynamic mode decomposition: an exact and tractable solution", this work provides additional details useful for building a compre...

Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based computation that generalizes a recent approach called "kernel-based dynamic mode decomposition". This new algori...

This work provides closed-form solutions and minimal achievable errors for a large class of low-rank approximation problems in Hilbert spaces. The proposed theorem generalizes to the case of linear bounded operators and p-th Schatten norms previous results obtained in the finite dimensional case for the Frobenius norm. The theorem is illustrated in...

We consider an enhanced version of the well-kwown "Petrov-Galerkin" projection in Hilbert spaces. The proposed procedure, dubbed "multi-slice" projector, exploits the fact that the sought solution belongs to the intersection of several high-dimensional slices. This setup is for example of interest in model-order reduction where this type of prior m...

This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach can be formalised as attempting to solve a low-rank constrained optimisation problem. This problem is non-convex and state-of-the-art algorithms are all sub-optimal....

This paper deals with model order reduction of parametrical dynamical systems. We consider the specific setup where the distribution of the system's trajectories is unknown but the following two sources of information are available: \textit{(i)} some "rough" prior knowledge on the system's realisations; \textit{(ii)} a set of "incomplete" observati...

In this work, we propose a novel procedure for video super-resolution, that is the recovery of a sequence of high-resolution images from its low-resolution counterpart. Our approach is based on a "sequential" model (i.e., each high-resolution frame is supposed to be a displaced version of the preceding one) and considers the use of sparsity-enforci...

The objective of this paper is to investigate how noisy and incomplete observations can be integrated in the process of building a reduced-order model. This problematic arises in many scientific domains where there exists a need for accurate low-order descriptions of highly-complex phenomena, which can not be directly and/or deterministically obser...

The objective of this paper is to investigate how noisy and incomplete observations can be integrated in the process of building a reduced-order model. This problematic arises in many scientific domains where there exists a need for accurate low-order descriptions of highly-complex phenomena, which can not be directly and/or deterministically obser...

Following recent contributions in non-linear sparse representations, this work focuses on a particular non-linear model, defined as the nested composition of functions. Recalling that most linear sparse representation algorithms can be straightforwardly extended to non-linear models, we emphasize that their performance highly relies on an efficient...

Based on physical laws describing the multiscale structure of turbulent flows, this paper proposes a regularizer for fluid motion estimation from an image sequence. Regularization is achieved by imposing some scale invariance property between histograms of motion increments computed at different scales. By reformulating this problem from a Bayesian...

Expanding on a wavelet basis the solution of an inverse problem provides several advantages. First of all, wavelet bases yield a natural and efficient multireso-lution analysis which allows defining clear optimization strategies on nested subspaces of the solution space. Be-sides, the continuous representation of the solution with wavelets enables...

This work is concerned with the ill-posed inverse problem of estimating turbulent flows from the observation of an image sequence. From a Bayesian perspective, a divergence-free isotropic fractional Brownian motion (fBm) is chosen as a prior model for instantaneous turbulent velocity fields. This self-similar prior characterizes accurately second-o...

Results of the application of optical flow methods to eye-safe aerosol lidar images leading to dense velocity field estimations are presented. A fluid motion dedicated for-mulation is employed, taking into account the deform-ing shapes and changing brightness of flow visualization. The optical flow technique has the advantage of provid-ing a vector...

A B S T R A C T In the context of tackling the ill-posed inverse problem of motion estimation from image sequences, we propose to introduce prior knowledge on flow regularity given by turbulence statistical models. Prior regularity is formalised using turbulence power laws describing statistically self-similar structure of motion increments across...

This article describes the implementation of a simple wavelet-based optical-flow motion estimator dedicated to continuous motions such as fluid flows. The wavelet representation of the unknown velocity field is considered. This scale-space represen-tation, associated to a simple gradient-based optimization algorithm, sets up a well-defined multires...

This work is concerned with the ill-posed inverse problem of estimating turbulent flows from the observation of an image sequence. From a Bayesian perspective, a divergence-free isotropic fractional Brownian motion (fBm) is chosen as a prior model for instantaneous turbulent velocity fields. This self-similar prior characterizes accurately second-o...

Selecting optimal models and hyperparameters is crucial for accurate optical-flow estimation. This paper provides a solution to the problem in a generic Bayesian framework. The method is based on a conditional model linking the image intensity function, the unknown velocity field, hyperparameters, and the prior and likelihood motion models. Inferen...

In the context of turbulent fluid motion measure-ment from image sequences, we propose in this paper to reverse the traditional point of view of wavelets per-ceived as an analyzing tool: wavelets and their proper-ties are now considered as prior regularization models for the motion estimation problem, in order to exhibit some well-known turbulence...

Based on a wavelet expansion of the velocity field, we present a novel optical flow algorithm dedicated to the estimation of continuous motion fields such as fluid flows. This scale-space representation, associated to a simple gradient-based optimization algorithm, naturally sets up a well-defined multi-resolution analysis framework for the optical...

Selecting optimal models and hyper-parameters is crucial for accurate optic-flow estimation. This paper solves the problem in a generic variational Bayesian framework. The method is based on a conditional model linking the image intensity function, the velocity field and the hyper-parameters characterizing the motion model. Inference is performed a...

Des centaines d'images nous parviennent chaque jour depuis les satellites d'observation de notre biosphère. Les modèles météorologiques et climatiques pourraient tirer grand bénéfice d'une meilleure exploitation de ces images et des informations qu'elles contiennent.

We consider a novel optic flow estimation algorithm based on a wavelet expansion of the velocity field. In particular, we propose an efficient gradient-based estimation algorithm which naturally encompasses the estimation process into a multiresolution framework while avoiding most of the drawbacks common to this kind of hierarchical methods. We th...

Des centaines d'images nous parviennent chaque jour depuis les satellites d'observation de notre biosphère. Les modèles météorologiques et climatiques pourraient tirer grand bénéfice d'une meilleur exploitation de ces images et des informations qu'elles contiennent.

Based on scaling laws describing the statistical structure of turbulent motion across scales, we propose a multiscale and non-parametric regularizer for optic-flow estimation. Regularization is achieved by constraining motion increments to behave through scales as the most likely self-similar process given some image data. In a first level of infer...

In this paper, Bayesian inference is used to select the most evident Gibbs prior model for motion estimation given some image sequence. The proposed method supplements the maximum a posteriori motion estimation scheme proposed in He¿as et al. (2008). Indeed, in this recent work, the authors have introduced a family of multiscale spatial priors in...

We propose a new multiscale PIV method based on turbulent kinetic energy decay. The technique is based on scaling power laws describing the statistical structure of turbulence. A spatial regularization constraints the solution to behave through scales as a self similar process via second-order structure function and a given power law. The real para...

The complexity of the laws of dynamics governing 3-D atmospheric flows associated with incomplete and noisy observations make the recovery of atmospheric dynamics from satellite image sequences very difficult. In this paper, we address the challenging problem of estimating physical sound and time-consistent horizontal motion fields at various atmos...

Based on scaling laws describing the statistical structure of turbulent motion across scales, we propose a multiscale and non-parametric regularizer for the estimation of velocity fields of bidimensional or quasi bidimensional flows from image sequences. Spatial regularization principle used in order to close the ill-posed nature of motion estimati...

Based on self-similar models of turbulence, we propose in this paper a multi-scale regularizer in order to provide a closure to the optic-flow estimation problem. Regularization is achieved by constraining motion increments to behave as a self-similar process. The associate constrained minimization problem results in a collection of first-order opt...

In this paper, we address the problem of estimating 3-D motions of a stratified atmosphere from satellite image sequences. The analysis of 3-D atmospheric fluid flows associated with incomplete observation of atmospheric layers due to the sparsity of cloud systems is very difficult. This makes the estimation of dense atmospheric motion field from s...

The complexity of dynamical laws governing 3D atmospheric flows associated with incomplete and noisy observations make the recovery of atmospheric dynamics from satellite images sequences very difficult. In this paper, we face the challenging problem of estimating physical sound and time-consistent horizontal motion fields at various atmospheric de...

We present in this paper a novel combined scheme dedicated to the measurement of velocity in fluid experimental flows through image sequences. The proposed technique satisfies the Navier–Stokes equations and combines the robustness of correlation techniques with the high density of global variational methods. It can be considered either as a reenfo...

In this paper, we address the problem of estimating three-dimensional motions of a stratified atmosphere from satellite image sequences. The complexity of three-dimensional atmospheric fluid flows associated to incomplete observation of atmospheric layers due to the sparsity of cloud systems makes very difficult the estimation of dense atmospheric...

In this paper, we address the problem of estimating mesoscale dynamics of atmospheric layers from satellite image sequences. Due to the great deal of spatial and temporal distortions of cloud patterns and because of the sparse 3-D nature of cloud observations, standard dense-motion field-estimation techniques used in computer vision are not well ad...

The complexity of dynamical laws governing 3D atmospheric flows associated to incomplete and noisy observations makes very difficult the recovery of atmospheric dynamics from satellite images sequences. In this paper, we face the challenging problem of joint estimation of time- consistent horizontal motion fields and pressure maps at various atmo-...

High resolution satellite image sequences are multidimensional signals composed of spatio-temporal patterns associated to numerous and various phenomena. Bayesian methods have been previously proposed in (Heas and Datcu, 2005) to code the information contained in satellite image sequences in a graph representation using Bayesian methods. Based on s...

Wepresentinthispaperanovelcollaborativesche- me dedicated to the measurement of velocity in fluid exper- imental flows through image sequences. The proposed tech- nique combine the robustness of correlation techniques with the high density of global variational methods. It can be con- sidered either as a reenforcement of fluid dedicated optical- fl...

In this paper, we address the problem of estimating mesoscale dynamics of atmospheric layers from satellite image sequences. Relying on a physically sound vertical decomposition of the atmosphere into lay- ers, we propose a dense motion estimator dedicated to the extraction of multi-layer horizontal wind elds. This estimator is expressed as the min...

Ce travail présente une nouvelle approche collaborative dédiée à la mesure de la vitesse en mécanique des fluides expérimentale à partir d’une séquence d’images d’un écoulement. La technique proposée combine la robustesse des méthodes de corrélation avec la grande densité d’information fournie par les méthodes variationnelles. En analyse du mouveme...

In this paper, we face the challenging problem of estimation of time-consistent layer motion fields at various atmospheric depths. Based on a vertical decomposition of the atmosphere, we propose three different dense motion estimator relying on multi-layer dynamical models. In the first method, we propose a mass conservation model which constitutes...

In this paper, we address the problem of estimating dense motion fields related to a stratified atmosphere which is ob- served through satellite imagery. Estimating the evolving vertical distribution of horizontal wind fields from satellite image time series is of great importance for the study of at- mospheric dynamics. Because of the sparse 3-dim...

During the last decades, satellites have acquired incessantly high-resolution images of many Earth observation sites. New products have arisen from this intensive acquisition process: high-resolution satellite image time-series (SITS). They represent a large data volume with a rich information content and may open a broad range of new applications....

Satellite image time‐series (SITS) are multidimensional signals of high complexity. Their main characteristics are spatio‐temporal patterns which describes the scene dynamics. The information contained in SITS was coded using Bayesian methods, resulting in a graph representation. This paper further presents a concept of interactive learning for sem...

The process of searching and analyzing data in order to discover potentially useful information is a crucial matter when dealing with large databases. Considering the huge amount of data collected by satellite observation systems, opportunities to generate multispectral image time-series are increasing. Exploratory methods are needed to understand...

A visual information mining concept is proposed for spatio-temporal patterns discovery in remotely sensed image time-series (ITS). An information theory framework is adopted to first model information content. It results in the inference of a relevant directed graph characterizing ITS. Then the user conjecture is modeled via visual information repr...

In this paper, a dynamic scene understanding concept is proposed and applied on multispectral image time series. Information mining enables the explorations and discovery of spatio temporal patterns localized in given spatio temporal windows. With this in mind, a hierarchical information representation is developed. It comprises different levels in...

In this paper, we describe an application of a scalespace clustering algorithm (melting) for exploration of image information content. Clustering by melting considers the feature space as a thermodynamical ensemble and groups the data by minimizing the free energy, having the temperature as a scale parameter. We develop clustering by melting for mu...

Images are highly complex multidimensional signals, with rich and complicated information content. For this reason they are difficult to analyze through a unique automated approach. However, a hierarchical representation is helpful for the understanding of image content. In this paper, we describe an application of a scale-space clustering algorith...

In this paper, we aim at facing the problem of estimating time consistent mesoscale dynamics of atmospheric layers from satellite image sequences. Due to the sudden variations of the luminance function observed within clouds patterns and which are caused by the intrinsic sparse 3-dimensional nature of clouds, the estimation of accurate dense motion...

This presentation is one of the first intercomparisons between vector fields representing atmospheric motions produced by different methods. Several methods extracting dense motion vector fields based mainly on optical flow techniques have been applied to a dataset of Meteosat Second Generation (MSG) images. The resulting vector fields have then be...

A method based on optical flow techniques has been developed at IRISA to compute dense motion vector fields from images (Corpetti et al., 2002). This method has been applied on consecutive MSG images in the thermal infrared (IR 10.8 µm) channel. Adaptations of the method consist in using a cloud classification to calculate "locally dense" vector fi...

The complexity of dynamical laws governing 3D atmospheric flows associated to incomplete and noisy observations makes very difficult the recovery of atmospheric dynamics from satellite images sequences. In this paper, we face the challenging problem of estimation of time-consistent layer motion fields at various atmospheric depths. Based on a verti...