Publications

2019

• Harder-Narasimhan theory for linear codes (with an appendix on Riemann-Roch theory)
  
  • Randriambololona Hugues
  J. Pure Appl. Algebra, 2019.
• Minimal Linear codes with few weights and their secret sharing.
  
  • Mesnager Sihem
  • Sinak A.
  • Yayla O.
  International Journal of Information Security Science, 2019.
• On the nonlinearity of Boolean functions with restricted input.
  
  • Mesnager Sihem
  • Zhou Z.
  • Ding C.
  Journal of Cryptography and Communications- Discrete Structures, Boolean Functions, and Sequences, 2019.
• Ratio-Based Multitemporal SAR Images Denoising: RABASAR
  
  • Zhao Weiying
  • Deledalle Charles-Alban
  • Denis Loïc
  • Maître Henri
  • Nicolas Jean-Marie
  • Tupin Florence
  IEEE Transactions on Geoscience and Remote Sensing, Institute of Electrical and Electronics Engineers, 2019. In this paper, we propose a fast and efficient multitemporal despeckling method. The key idea of the proposed approach is the use of the ratio image, provided by the ratio between an image and the temporal mean of the stack. This ratio image is easier to denoise than a single image thanks to its improved stationarity. Besides, temporally stable thin structures are well preserved thanks to the multi-temporal mean. The proposed approach can be divided into three steps: 1) estimation of a “super-image” by temporal averaging and possibly spatial denoising; 2) denoising of the ratio between the noisy image of interest and the “super-image”; 3) computation of the denoised image by re-multiplying the denoised ratio by the “super-image”. Because of the improved spatial stationarity of the ratio images, denoising these ratio images with a speckle-reduction method is more effective than denoising images from the original multi-temporal stack. The amount of data that is jointly processed is also reduced compared to other methods through the use of the “super-image” that sums up the temporal stack. The comparison with several state-of-the-art reference methods shows better results numerically (peak signal-noise-ratio, structure similarity index) as well as visually on simulated and SAR time series. The proposed ratio-based denoising framework successfully extends single-image SAR denoising methods to time series by exploiting the persistence of many geometrical structures. (10.1109/TGRS.2018.2885683)
  DOI : 10.1109/TGRS.2018.2885683
• Some Results About a Conjecture on Identifying Codes in Complete Suns
  
  • Hudry Olivier
  • Lobstein Antoine
  International Transactions in Operational Research, Wiley, 2019, 26 (2), pp.732-746. Consider a graph G = (V, E) and, for every vertex v ∈ V , denote by B(v) the set {v} ∪ {u : uv ∈ E}. A subset C ⊆ V is an identifying code if the sets B(v) ∩ C, v ∈ V , are all nonempty and distinct. It is a locating-dominating code if the sets B(v) ∩ C, v ∈ V \ C, are all nonempty and distinct. Let S n be the graph whose vertex set can be partitioned into two sets U n and V n , where U n = {u 1 , u 2 ,. .. , u n } induces a clique, and V n = {v 1,2 , v 2,3 ,. .. , v n−1,n , v n,1 } induces an independent set, with edges v i,i+1 u i and v i,i+1 u i+1 , 1 ≤ i ≤ n; computations are carried modulo n. This graph is called a complete sun. We prove the conjecture, stated by Argiroffo, Bianchi and Wagler in 2014, that the smallest identifying code in S n has size equal to n. We also characterize and count all the identifying codes with size n in S n. Finally, we determine the sizes of the smallest locating-dominating codes in S n . (10.1111/itor.12320)
  DOI : 10.1111/itor.12320
• Etude exploratoire du réseau nerveux pelvien par tractographie
  
  • Muller C.
  • Delmonte A.
  • Meignan P.
  • Peyrot Q.
  • Virzi A.
  • Berteloot L.
  • Grevent D.
  • Blanc T.
  • Gori P.
  • Boddaert N.
  • Bloch Isabelle
  • Sarnacki S.
  , 2019.
• From Structuring Elements to Structuring Neighborhood Systems
  
  • Goy Alexandre
  • Aiguier Marc
  • Bloch Isabelle
  , 2019, LNCS 11564, pp.16-28. In the context of mathematical morphology based on structuring elements to define erosion and dilation, this paper generalizes the notion of a structuring element to a new setting called structuring neighborhood systems. While a structuring element is often defined as a subset of the space, a structuring neighborhood is a subset of the subsets of the space. This yields an extended definition of erosion; dilation can be obtained as well by a duality principle. With respect to the classical framework, this extension is sound in many ways. It is also strictly more expressive, for any structuring element can be represented as a structuring neighborhood but the converse is not true. A direct application of this framework is to generalize modal morpho-logic to a topological setting. (10.1007/978-3-030-20867-7_2)
  DOI : 10.1007/978-3-030-20867-7_2
• Relay Placement for Reliable Ranging in Cooperative mm-Wave Systems
  
  • Ghatak Gourab
  • de Domenico Antonio
  • Coupechoux Marceau
  IEEE Wireless Communications Letters, IEEE comsoc, 2019, 8 (5), pp.1324-1327. We study millimeter wave based ranging of randomly located terminal nodes (TN) using fixed relay nodes (RN) deployed around a central node (CN). This setting may correspond to a disaster-relief scenario where the rescuers require positioning information in the absence of a global positioning system (GPS). We derive the Bayesian Cramer-Rao lower bound (BCRLB) for the TNs range estimation from the CN as well as from the RNs in this network using a stochastic geometry framework. Contrary to existing studies, we take the effect of link-blockages into account while deriving the BCRLB, and thereby present a more accurate bound on the ranging error. For the special case of no blockages, we formulate a convex problem for obtaining the optimal relay positions. Our results provide the operator a guideline for initial deployment planning, in terms of number and location of RNs to be deployed in order to achieve an accurate ranging. (10.1109/LWC.2019.2915824)
  DOI : 10.1109/LWC.2019.2915824
• Logical Dual Concepts based on Mathematical Morphology in Stratified Institutions
  
  • Aiguier Marc
  • Bloch Isabelle
  Journal of Applied Non-Classical Logics, Taylor & Francis, 2019, 29 (4), pp.392-429. Several logical operators are defined as dual pairs, in different types of logics. Such dual pairs of operators also occur in other algebraic theories, such as mathematical morphology. Based on this observation, this paper proposes to define, at the abstract level of institutions, a pair of abstract dual and logical operators as morphological erosion and dilation. Standard quantifiers and modalities are then derived from these two abstract logical operators. These operators are studied both on sets of states and sets of models. To cope with the lack of explicit set of states in institutions, the proposed abstract logical dual operators are defined in an extension of institutions, the stratified institutions, which take into account the notion of open sentences, whose satisfaction is parametrised by sets of states. A hint on the potential interest of the proposed framework for spatial reasoning is also provided. (10.1080/11663081.2019.1668678)
  DOI : 10.1080/11663081.2019.1668678
• Pruning neural networks thanks to morphological layers
  
  • Blusseau Samy
  • Zhang Yunxiang
  • Velasco-Forero Santiago
  • Bloch Isabelle
  • Angulo Jesus
  , 2019, pp.17. Motivated by recent advances in morphological neural networks, we further study the properties of morphological units when incorporated in layers of conventional neural networks. We confirm and extend the observation that a Max-plus layer can be used to select relevant filters and reduce redundancy in its previous layer, without incurring performance loss. We present several experiments in image processing, showing that this filter selection property seems efficient and robust. We also point out the close connection between Maxout networks and our pruned Max-plus networks. The code related to our experiments is available online (https://github.com/yunxiangzhang).
• Structural information and (hyper)graph matching for MRI piglet brain extraction
  
  • Durandeau Alexandre
  • Fasquel Jean-Baptiste
  • Bloch Isabelle
  • Mazerand Edouard
  • Menei Philippe
  • Montero-Menei Claudia
  • Dinomais Mickaël
  , 2019, pp.76-81. In the context of the study of the maturation process of the infant brain, this paper focuses on postnatal piglet brain, whose structure is similar to the one of an infant. Due to the small size of the piglet brain and the abundance of surrounding fat and muscles, the automatic brain extraction using correctely initialized deformable models is tedious, and the standard approach used for human brain does not apply. The paper proposes an original brain extraction method based on a deformable model, whose initialization is guided by a priori known relationships between some anatomical structures of the head. This concerns a structural model related to a priori known inclusion and photometric relationships between eyes, nose and other internal head entities (fat and muscles). This a priori structural information also involves the relative position of both eyes and nose, assumed to be an anatomical invariant similar to a triangle. Using this structural model, our proposal detects both eyes and nose, from which one deduces the brain center, for finally initializing deformable models. Anatomical structures are retrieved by matching observed relationships with those embedded in the a priori structural model. This involves graph and hypergraph matching, where hypergraph matching concerns relative position of eyes and nose (ternary constraint related to these 3 entities). The method has been implemented and preliminary experiments have been performed on a set of 6 piglets, to evaluate the accuracy of the brain center localization, the one of the final brain extraction using deformable models. The brain center is correctly localized with a mean error of 1.7 mm, underlying the relevance of the approach. The mean similarity index has been measured to be of 0.85 (with a standard deviation of 0.04). More generally, this work illustrates the potential of considering high level a priori known relationships, related to anatomical invariants, managed using graph and hypergraph matching.
• Robust Segmentation of Corpus Callosum in Multi-Scanner Pediatric T1-w MRI using Transfer Learning
  
  • La Barbera Giammarco
  • Bloch Isabelle
  • Barraza Gonzalo
  • Adamsbaum Catherine
  • Gori Pietro
  , 2019.
• A Simple and Exact Algorithm to Solve Linear Problems with l1 -based Regularizers
  
  • Tendero Yohann
  • Ciril Igor
  • Darbon Jérôme
  , 2019.
• A Review of Sparse Recovery Algorithms
  
  • Crespo Marques Elaine
  • Maciel Nilson
  • Naviner Lirida
  • Cai Hao
  • Yang Jun
  IEEE Access, IEEE, 2019, 7, pp.1300-1322. Nowadays, a large amount of information has to be transmitted or processed. This implies high-power processing, large memory density, and increased energy consumption. In several applications, such as imaging, radar, speech recognition, and data acquisition, the signals involved can be considered sparse or compressive in some domain. The compressive sensing theory could be a proper candidate to deal with these constraints. It can be used to recover sparse or compressive signals with fewer measurements than the traditional methods. Two problems must be addressed by compressive sensing theory: design of the measurement matrix and development of an efficient sparse recovery algorithm. These algorithms are usually classified into three categories: convex relaxation, non-convex optimization techniques, and greedy algorithms. This paper intends to supply a comprehensive study and a state-of-the-art review of these algorithms to researchers who wish to develop and use them. Moreover, a wide range of compressive sensing theory applications is summarized and some open research challenges are presented. (10.1109/ACCESS.2018.2886471)
  DOI : 10.1109/ACCESS.2018.2886471
• Codes, Cryptology and Information Security
  
  • Carlet Claude
  • Guilley Sylvain
  • Nitaj Abderrahmane
  • Souidi El Mamoun
  , 2019. (10.1007/978-3-030-16458-4)
  DOI : 10.1007/978-3-030-16458-4
• Seq2VAR: multivariate time series representation with relational neural networks and linear autoregressive model
  
  • Pineau Edouard
  • Razakarivony Sebastien
  • Bonald Thomas
  , 2019. Finding understandable and meaningful feature representation of multivariate time series (MTS) is a difficult task, since information is entangled both in temporal and spatial dimensions. In particular, MTS can be seen as the observation of simultaneous causal interactions between dynamical variables. Standard way to model these interactions is the vector linear autoregression (VAR). The parameters of VAR models can be used as MTS feature representation. Yet, VAR cannot generalize on new samples, hence independent VAR models must be trained to represent different MTS. In this paper, we propose to use the inference capacity of neural networks to overpass this limit. We propose to associate a relational neural network to a VAR generative model to form an encoder-decoder of MTS. The model is denoted Seq2VAR for Sequence-to-VAR. We use recent advances in relational neural network to build our MTS encoder by explicitly modeling interactions between variables of MTS samples. We also propose to leverage reparametrization tricks for binomial sampling in neural networks in order to build a sparse version of Seq2VAR and find back the notion of Granger causality defined in sparse VAR models. We illustrate the interest of our approach through experiments on synthetic datasets.
• Tree Sampling Divergence: An Information-Theoretic Metric for Hierarchical Graph Clustering
  
  • Charpentier Bertrand
  • Bonald Thomas
  , 2019. We introduce the tree sampling divergence (TSD), an information-theoretic metric for assessing the quality of the hierarchical clustering of a graph. Any hierarchical clustering of a graph can be represented as a tree whose nodes correspond to clusters of the graph. The TSD is the Kullback-Leibler divergence between two probability distributions over the nodes of this tree: those induced respectively by sampling at random edges and node pairs of the graph. A fundamental property of the proposed metric is that it is interpretable in terms of graph reconstruction. Specifically, it quantifies the ability to reconstruct the graph from the tree in terms of information loss. In particular, the TSD is maximum when perfect reconstruction is feasible, i.e., when the graph has a hierarchical structure and can be reconstructed exactly from the corresponding tree. Another key property of TSD is that it applies to any tree, not necessarily binary. In particular, the TSD applies to trees of height 2, corresponding to the case of usual clustering (not hierarchical) whose output is a partition of the set of nodes. The TSD can thus be viewed as a universal metric, applicable to any type of clustering. Moreover, the TSD can be used in practice to compress a binary tree while minimizing the information loss in terms of graph reconstruction, so as to get a compact representation of the hierarchical structure of a graph. We illustrate the behavior of TSD compared to existing metrics on experiments based on both synthetic and real datasets.
• Almost surely constrained convex optimization
  
  • Fercoq Olivier
  • Alacaoglu Ahmet
  • Necoara Ion
  • Cevher Volkan
  , 2019, 97, pp.1910-1919. We propose a stochastic gradient framework for solving stochastic composite convex optimization problems with (possibly) infinite number of linear inclusion constraints that need to be satisfied almost surely. We use smoothing and homotopy techniques to handle constraints without the need for matrix-valued projections. We show for our stochastic gradient algorithm $\mathcal{O}(\log(k)/\sqrt{k})$ convergence rate for general convex objectives and $\mathcal{O}(\log(k)/k)$ convergence rate for restricted strongly convex objectives. These rates are known to be optimal up to logarithmic factors, even without constraints. We demonstrate the performance of our algorithm with numerical experiments on basis pursuit, a hard margin support vector machines and a portfolio optimization and show that our algorithm achieves state-of-the-art practical performance.
• Addressing Failure and Aging Degradation in MRAM/MeRAM-on-FDSOI Integration
  
  • Cai Hao
  • Wang You
  • Naviner Lirida
  • Liu Xinning
  • Shan Weiwei
  • Yang Jun
  • Zhao Weisheng
  IEEE Transactions on Circuits and Systems I: Regular Papers, IEEE, 2019, 66 (1), pp.239-250. (10.1109/TCSI.2018.2854277)
  DOI : 10.1109/TCSI.2018.2854277
• Algorithmes gloutons avec la classe
  
  • Zayana Karim
  • Michalak Pierre
  • Beauseigneur Clément
  • Tanoh Hélène
  , 2019. Les algorithmes gloutons offrent une solution pratique, mais pas toujours optimale, à de nombreux problèmes arithmétiques. Nous en donnons ici deux exemples (fractions égyptiennes et algorithme du monnayeur) avant d'entrer dans des considérations plus théoriques.
• Towards Interpretability of Segmentation Networks by analyzing DeepDreams
  
  • Couteaux Vincent
  • Nempont O.
  • Pizaine Guillaume
  • Bloch Isabelle
  , 2019, LCNS 11797, pp.56-63. Interpretability of a neural network can be expressed as the identification of patterns or features to which the network can be either sensitive or indifferent. To this aim, a method inspired by DeepDream is proposed, where the activation of a neuron is maximized by performing gradient ascent on an input image. The method outputs curves that show the evolution of features during the maximization. A controlled experiment show how it enables assess the robustness to a given feature, or by contrast its sensitivity. The method is illustrated on the task of segmenting tumors in liver CT images.
• Optimal survey schemes for stochastic gradient descent with applications to M-estimation
  
  • Clémençon Stéphan
  • Bertail Patrice
  • Chautru Emilie
  • Papa Guillaume
  ESAIM: Probability and Statistics, EDP Sciences, 2019, 23, pp.310-337. Iterative stochastic approximation methods are widely used to solve M-estimation problems, in the context of predictive learning in particular. In certain situations that shall be undoubtedly more and more common in the Big Data era, the datasets available are so massive that computing statistics over the full sample is hardly feasible, if not unfeasible. A natural and popular approach to gradient descent in this context consists in substituting the “full data” statistics with their counterparts based on subsamples picked at random of manageable size. It is the main purpose of this paper to investigate the impact of survey sampling with unequal inclusion probabilities on stochastic gradient descent-based M-estimation methods. Precisely, we prove that, in presence of some a priori information, one may significantly increase statistical accuracy in terms of limit variance, when choosing appropriate first order inclusion probabilities. These results are described by asymptotic theorems and are also supported by illustrative numerical experiments. (10.1051/ps/2018021)
  DOI : 10.1051/ps/2018021
• Progressive hologram transmission using a view-dependent scalable compression scheme
  
  • Rhammad Anas El
  • Gioia Patrick
  • Gilles Antonin
  • Cagnazzo Marco
  Annals of Telecommunications - annales des télécommunications, Springer, 2019. Over the last few years, holography has been emerging as an alternative to stereoscopic imaging since it provides users with the most realistic and comfortable three-dimensional (3D) experience. However, high quality holograms enabling a free-viewpoint visualization contain tremendous amount of data. Therefore, a user willing to access to a remote hologram repository would face high downloading time, even with high speed networks. To reduce transmission time, a joint viewpoint-quality scalable compression scheme is proposed. At the encoder side, the hologram is first decomposed into a sparse set of diffracted light rays using Matching Pursuit over a Gabor atoms dictionary. Then, the atoms corresponding to a given user's viewpoint are selected to form a sub-hologram. Finally, the pruned atoms are sorted and encoded according to their importance for the reconstructed view. The proposed approach allows a progressive decoding of the sub-hologram from the first received atom. Streaming simulations for a moving user reveal that our approach outperforms conventional scalable codecs such as scalable H.265 and enables a practical streaming with a better quality of experience.
• Improved Small Molecule Identification through Learning Combinations of Kernel Regression Models
  
  • Brouard Celine
  • Bassé Antoine
  • d'Alché-Buc Florence
  • Rousu Juho
  Metabolites, MDPI, 2019, 9 (8), pp.160. In small molecule identification from tandem mass (MS/MS) spectra, input–output kernel regression (IOKR) currently provides the state-of-the-art combination of fast training and prediction and high identification rates. The IOKR approach can be simply understood as predicting a fingerprint vector from the MS/MS spectrum of the unknown molecule, and solving a pre-image problem to find the molecule with the most similar fingerprint. In this paper, we bring forward the following improvements to the IOKR framework: firstly, we formulate the IOKRreverse model that can be understood as mapping molecular structures into the MS/MS feature space and solving a pre-image problem to find the molecule whose predicted spectrum is the closest to the input MS/MS spectrum. Secondly, we introduce an approach to combine several IOKR and IOKRreverse models computed from different input and output kernels, called IOKRfusion. The method is based on minimizing structured Hinge loss of the combined model using a mini-batch stochastic subgradient optimization. Our experiments show a consistent improvement of top-k accuracy both in positive and negative ionization mode data (10.3390/metabo9080160)
  DOI : 10.3390/metabo9080160
• Gaps between prime numbers and tensor rank of multiplication in finite fields
  
  • Randriambololona Hugues
  Designs, Codes and Cryptography, Springer Verlag, 2019.