S³ - Inverse problems in signal and image processing and S³ - Bayesian inference framework: from basic to advanced Bayesian computation

Séminaire le 27 Mars 2015, 10h30 à CentraleSupelec (Gif-sur-Yvette) Salle des séminaires du L2S
Ali Mohammad Djafari, CNRS, L2S

In signal and image processing community, we can distinguish two categories:
- Those who start from the observed signals and images and do classical processing: filtering for denoising, change detection, contour detection, segmentation, compression, …
- The second category called “model based”, before doing any processing try first to understand from where those signals and images come from and why they are here . So, first defining what quantity has been at the origin of those observations, then modeling their link by “forward modeling” and finally doing inversion. This approach is often called “Inverse problem approach”. Then, noting the “ill-posedness” of the inverse problems, many “Regularization methods” have been proposed and applied successfully. However, deterministic regularization has a few limitations and recently the Bayesian inference approach has become the main approach for proposing unsupervised methods and effective solutions in many real applications. Interestingly, even many classical methods have found better understanding when re-stated as inverse problem. The Bayesian approach with simple prior models such as Gaussian, Generalized Gaussian, Sparsity
enforcing priors or more sophisticated Hierarchical models such as Mixture models, Gaussian Scale Mixture or Gauss-Markov-Potts models have been proposed in different applications of imaging systems with great success. However, Bayesian computation still is too costly and need more practical algorithms than MCMC. Variational Bayesian Approximation (VBA) methods have recently became a standard for computing the posterior means in unsupervized methods.
Interestingly, we show that VBA includes Joint Maximum A Posteriori (JMAP) and Expectation-Maximization (EM) as special cases. VBA is much faster than MCMC methods, but, it gives only access to the posterior means.
This talk gives an overview of these methods with examples in Deconvolution (simple or blind, signal or image) and  in Computed Tomography (CT).

Bio: http://djafari.free.fr/index.htm

Séminaire S³

PDE-­‐based inversion method with no forward solver for inverse medium scattering problems

Séminaire le 20 Mars 2015, 14h00 à CentraleSupelec (Gif-sur-Yvette) Salle du conseil du L2S - B4.40
Dr. Yu Zhong

Bio: Dr. Yu Zhong received his B.S. and M.S. degrees in electronic engineering from Zhejiang University, Hangzhou, China, in 2003 and 2006, respectively, and the Ph.D. degree from the National University of Singapore, Singapore, in 2010.
He is currently a Scientist in Institution of High Performance Computing (IHPC), A*STAR, Singapore.
His research interests mainly are inverse-­‐scattering problems and electromagnetic modeling on composite materials. He is a regular visitor at the Laboratoire des Signaux et Systèmes (L2S) in Gif-­sur-­‐Yvette, France as an invited senior scientific expert since 2012.
Talk 1: PDE-­‐based inversion method with no forward solver for inverse medium scattering problems
A new partial differential equation (PDE) based inversion method for inverse medium scattering problems is proposed in this talk, which does not need to solve any forward problem. The proposed method is the subspace-­‐based optimization method (SOM) in the differential-­‐equation frame. The finite difference scheme is used to discretized the Helmholtz equation, and the twofold subspace-­‐based regularization scheme, as in the integral equation based SOM, is applied in this PDE-­‐based inversion method to stabilize the solver. By using such a PDE-­‐based inversion method, the Green’s funciton for the domain of interests is no longer needed. Representative numerical tests are presented to verify the efficacy of the proposed method.

Talk 2: New integral equation and new partial differential equation for inverse medium scattering problems with strong scatterers 

In this talk, we propose two new equations, an integral equation (IE) and a partial differential equation (PDE), for solving inverse medium scattering problems (IMSP) with strong scatterers. First, we present a new integral equation, which could effectively reduce the globle wave contribution in estimating the contrast (the difference between permittivities of the scatterers and the known background) compared to the original Lippmann-­‐Schwinger equation. Using such a new IE in the IE-­‐based inversion method one is able to solve the highly nonlinear IMSP with strong scatterers.
Subsequently, the connection between the PDE-­‐based inversion method (in Talk 1), using the Helmholtz equation, and the conventional IE based inversion method, using the Lippmann-­‐Schwinger equation, is discussed. With such a connection and the new IE, we propose a new PDE,
using which the PDE-­‐based inversion method can also solve the highly nonlinear IMSP. At last, we discuss the pros and cons of both PDE-­‐ and IE-­‐based inversion methods.

S³ - Analysis of remote sensing multi-sensor heterogeneous images

Séminaire le 20 Mars 2015, 10h30 à CentraleSupelec (Gif-sur-Yvette) Salle des séminaires du L2S
Jorge Prendes, IRIT Toulouse and SONDRA CentraleSupelec

Remote sensing images are images of the Earth acquired from planes or satellites. In recent years the technology enabling this kind of images has been evolving really fast. Many different sensors have been developed to measure different properties of the earth surface, including optical images, SAR images and hyperspectral images. One of the interest of this images is the detection of changes on datasets of multitemporal images. Change detection has been thoroughly studied on the case where the dataset consist of images acquired by the same sensor. However, having to deal with datasets containing images acquired from different sensors (heterogeneous images) is becoming very common nowadays.
In order to deal with heterogeneous images, we proposed a statistical model which describe the joint distribution of the pixel intensity of the images, more precisely a mixture model. On unchanged areas, we expect the parameter vector of the model to belong to a manifold related to the physical properties of the objects present on the image, while on areas presenting changes this constraint is relaxed. The distance of the model parameter to the manifold can be thus be used as a similarity measure, and the manifold can be learned using ground truth images where no changes are present. The model parameters are estimated through a collapsed Gibbs sampler using a Bayesian non parametric approach combined with a Markov random field.
In this talk I will present the proposed statistical model, its parameter estimation, and the manifold learning approach. The results obtained with this method will be compared with those of other classical similarity measures.

Bio: Jorge Prendes was born in Santa Fe, Argentina in 1987. He received the 5 years Eng. degree in Electronics Engineering with honours from the Buenos Aires Institute of Technology (ITBA), Buenos Aires, Argentina in July 2010. He worked on Signal Processing at ITBA within the Applied Digital Electronics Group (GEDA) from July 2010 to September 2012. Currently he is a Ph.D. student in Signal Processing in SONDRA laboratory at Supélec, within the cooperative laboratory TéSA and the Signal and Communication Group of the Institut de Recherche en Informatique de Toulouse (IRIT). His main research interest include image processing, applied mathematics and pattern recognition.


Séminaire S³

S³: Rare event simulation: a Point Process interpretation with application in probability and quantile estimati

Séminaire le 13 Mars 2015, 10h00 à CentraleSupelec (Gif-sur-Yvette) Salle des séminaires du L2S
Clément Walter, CEA and University Paris Diderot

Clément Walter, 25, graduated from Mines ParisTech in 2013. Beforehand he attended preparatory classes in Lycée Sainte-Geneviève (branch Maths and Physics). For his master degree he specialised in Geostatistics and started working with CEA as an intern on emulation of complex computer codes (especially kriging) for rare event simulation and estimation. He has then pursued his work in a PhD under the direction of Pr. Josselin Garnier, focusing on multilevel splitting methods.

S³ Bayesian Tomography

Séminaire le 6 Mars 2015, 10h00 à CentraleSupelec (Gif-sur-Yvette) Salle des séminaires du L2S
John Skilling, Maximum Entropy Data Consultants Ltd, UK

Bio: John Skilling was awarded his PhD in radio astronomy in 1969.  Through the 1970s and 1980s he was a lecturer in applied mathematics at Cambridge University, specialising in data analysis.  He left to concentrate on consultancy work, originally using maximum entropy methods but moving to Bayesian methodology when algorithms became sufficiently powerful.  John has been a prominent contributor to the “MaxEnt” conferences since their beginning in 1981.  He is the discoverer of the nested sampling algorithm which performs integration over spaces of arbitrary dimension, which is the basic operation dictated by the sum rule of Bayesian calculus.

Séminaire S³

S³ L0 optimization for DOA and sparse channel estimation

Séminaire le 6 Mars 2015, 10h00 à CentraleSupelec (Gif-sur-Yvette) Salle des séminaires du L2S
Adilson Chinatto, Univeristy of Campinas, BR and Ecole Normale Supérieure de Cachan, FR

Bio: Adilson Chinatto received a degree in Electrical Engineering in 1997 and Masters in 2011, both from the University of Campinas (Unicamp), Brazil. He worked as hardware, software and firmware development engineer for optical transmission equipment in the companies AsGa and CPqD in Brazil. He is a co-founder of Espectro Ltd., a Brazilian design house for hardware and software, focused in signal processing. Nowadays he is coordinator of a High Performance GPS Receiver Project at Espectro Ltd. funded by the Brazilian National Counsel of Technological and Scientific Development (CNPq). He has experience in electrical engineering with emphasis on telecommunication systems, digital signal processing and smart antennas, working mainly with development and implementation of programmable logic devices (FPGA). He is currently finishing his Ph.D. at Unicamp, working with sparse and compressive sensing signal processing.

Séminaire S³

S³ Correlation mining in high dimension with limited samples

Séminaire le 30 Janvier 2015, 10h30 à CentraleSupelec (Gif-sur-Yvette) Salle des séminaires du L2S
Alfred Hero

Alfred Hero:
Title: Correlation mining in high dimension with limited samples 

Abstract: Correlation mining arises in many areas of engineering, social sciences, and natural sciences. Correlation mining discovers columns of a random matrix that are highly correlated with other columns of the matrix and can be used to construct a dependency network over columns. However, when the number n of samples is finite and the number p of columns increases such exploration becomes futile due to a phase transition phenomenon: spurious discoveries will eventually dominate. In this presentation I will present theory for predicting these phase transitions and present Poisson limit theorems that can be used to determine finite sample behavior of correlation structure. The theory has application to areas including gene expression analysis, network security, remote sensing, and portfolio selection. 

BioAlfred O. Hero III received the B.S. (summa cum laude) from Boston University (1980) and the Ph.D from Princeton University (1984), both in Electrical Engineering. Since 1984 he has been with the University of MichiganAnn Arbor, where he is the R. Jamison and Betty Williams Professor of Engineering. His primary appointment is in the Department of Electrical Engineering and Computer Science and he also has appointments, by courtesy, in the Department of Biomedical Engineering and the Department of Statistics. From 2008-2013 he was held the Digiteo Chaire d'Excellence at the Ecole Superieure d'Electricite, Gif-sur-Yvette, France. He is a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) and several of his research articles have recieved best paper awards. Alfred Hero was awarded the University of Michigan Distinguished Faculty Achievement Award (2011). He received the IEEE Signal Processing Society Meritorious Service Award (1998), the IEEE Third Millenium Medal (2000), and the IEEE Signal Processing Society Technical Achievement Award (2014). Alfred Hero was President of the IEEE Signal Processing Society (2006-2008) and was on the Board of Directors of the IEEE (2009-2011) where he served as Director of Division IX (Signals and Applications). Alfred Hero's recent research interests are in statistical signal processing, machine learning and the analysis of high dimensional spatio-temporal data. Of particular interest are applications to networks, including social networks, multi-modal sensing and tracking, database indexing and retrieval, imaging, and genomic signal processing.

György Terdik:
Title: A new covariance function for spatio-temporal data analysis with application to atmospheric pollution and sensor networking

Abstract: See the attached file.

Bio: György Terdik, received the Ph.D. degree from theKossuth Lajos University, Hungary. He is a Professor  of the Department of Information Technology at the University ofDebrecen, Hungary. His research areas include nonlinear, non-Gaussian time series analysis, Lévyprocesses, and high-speed network modeling, spatio-temporal time series, Dr. Terdik is a member of the editorial board of the

quarterly Publicationes Mathematicae Debrecen.

Márton Ispány:
Title Poisson INAR processes with serial and seasonal correlation 

Abstract: Recently, there has been considerable interest in integer-valued time series models.  Motivation to include discrete data models comes from the need to account for the discrete nature of certain data sets, often counts of events, objects or individuals. Among the most successful integer-valued time series models proposed in the literature we mention the INteger-valued AutoRegressive model of order p (INAR(p)). However, seasonal count processes have not been investigated yet, except one of our new papers. In the talk, we study INAR processes which possess serial and seasonal structure as well. The main properties of the models will be derived such as the stationarity and the autocorrelation function. The conditional least squares and conditional maximum likelihood estimators of the model parameters will be studied and their asymptotical properties will be established. In addition, we would like to discuss the case in which the marginal distributions are Poisson in detail. Monte 
Carlo experiments will be conducted to evaluate and compare the performance of various estimators for finite sample sizes. Real data set on the area of insurance will be applied to evaluate the model performance. 

Bio: Márton Ispány (https://it.inf.unideb.hu/honlap/ispanymarton/english) received the M.Sc.(1989) and PhD (summa cum laude) in Statistics (1997) from University of Debrecen. Since 2007 he has been with the  Department of Information Technology, Faculty of Informatics, University of Debrecen. Since 2012 he has been the head of the department. Márton Ispány 's recent research interests are in branching processes (functional limit theorems, asymptotics for conditional least squares estimation, integer valued autoregression), statistical modelling(generalized SVD, contaminated statistical models, EM algorithm), data mining (decision trees, stochastic algorithms, MCMC, web mining), and applied statistics: econometrics and insurance, cross-country modelling, statistical genetics.


Interval Analysis - Fundamentals and Electromagnetic Engineering Applications

Séminaire le 29 Janvier 2015, 14h00 à CentraleSupelec (Gif-sur-Yvette) Salle du conseil du L2S - B4.40
Paolo Rocca

Paolo Rocca received the MS degree in Telecommunications Engineering from the University of Trento in 2005 (summa cum laude) and the PhD Degree in Information and Communication Technologies from the same University in 2008. He is currently Assistant Professor at the Department of Information Engineering and Computer Science (University of Trento) and a member of the ELEDIA Research Center. Dr. Rocca is the author/co-author of over 230 peer reviewed papers on international journals and conferences. He has been a visiting Ph.D. student at the Pennsylvania State University (U.S.A.), at the University Mediterranea of Reggio Calabria (Italy), and a visiting researcher at the Laboratoire des Signaux et Systèmes (L2S@ Supélec, France) in 2012 and 2013. Moreover, he has been an Invited Associate Professor at the University of Paris Sud (France) in 2015. Dr. Rocca has been awarded from the IEEE Geoscience and Remote Sensing Society and the Italy Section with the best PhD thesis award IEEE-GRS Central Italy Chapter. His main interests are in the framework of antenna array synthesis and design, electromagnetic inverse scattering, and optimization techniques for electromagnetics. He serves as an Associate Editor of the IEEE Antennas and Wireless Propagation Letters.

Small Primitive Roots and Malleability of RSA Moduli

Séminaire le 13 Janvier 2015, 14h00 à CentraleSupelec (Gif-sur-Yvette) Salle du conseil du L2S - B4.40
Prof. Jorge Jimenez Urroz from Polytechnic University of Catalonia, Barcelona, Catalunya,

Prof. Jorge Jimenez Urroz from Polytechnic University of Catalonia, Barcelona, Catalunya, Spain will give a seminar at L2S, on Tuesday 13th January 2015, room F.3.09, Supélec, campus of Gif-sur-Yvette.

Title: Small Primitive Roots and Malleability of RSA Moduli

Abstract: We prove that factorization is a malleable problem, in the sense that given an RSA modulus n, partial information on another integer n' independent helps to factorize n.

List of publications : http://www-ma4.upc.edu/~jjimenez/papers.htm