#### Scheduling robotic tasks for industrial applications

The automation of robotic tasks in the aviation industry requires the development of techniques combining the automatic generation of movement elements to execute tasks with the optimal scheduling of these tasks. The Gepetto team at LAAS has a long experience in motion planning for systems with a large number of degrees of freedom in environments occupied by obstacles. The ROC team has a long experience in combinatorial optimization problems such as task scheduling, which is also the subject of the KC@ANITI chair.

The objective of this internship is to combine these techniques in order to produce

movements performing robotic tasks in optimal order. Two difficulties specific to this combination are:

1. the a priori ignorance of the cost of transition from one task to another,

2. the fact that a given task can be performed by an infinite number of configurations of the robot due to its kinematic redundancy.

The work will be illustrated by an application of drilled holes deburring in an Airbus A 320 reactor mast (picture above).

**REQUIRED SKILLS**

The candidate must have programming skills in python. Knowledge of C++ programming and combinatorial optimization will be appreciated.

**Stage de recherche Durée** : 4 à 6 mois

**Niveau d’études**: Master 2

#### Détection et délinéation automatique des parcelles de culture à partir des données Sentinel2

Pour les besoins des activités de recherche en cartographie de l’occupation du sol et de suivi des cultures réalisées au CESBIO (*www.cesbio.cnrs.fr*), il serait utile de disposer d’une méthodologie automatique permettant, à partir d’une série temporelle d’images Sentinel2, de produire une base de données géographique des parcelles agricoles.

> Consultez l’annonce en ligne sur le site du Cnes

**Stage ingénieur / master – Télédétection et Machine Learning,Durée** : 4 à 6 mois,

**temps plein**

**Niveau d’études**: Master, DESS, DEA, Bac+5/

#### Estimation of large-dimensional tensor models and applications in machine learning

**SUPERVISORS**

The internship will be supervised by Prof. H. Goulart (henrique.goulart@irit.fr) at IRIT/ENSEEIHT, in remote collaboration with two members of the LargeDATA (DataScience) chair at 3IA MIAI/Univ. Grenoble-Alpes : Prof. R. Couillet (head, romain.couillet@gipsa-lab.grenobleinp.fr) and Dr. P. Comon (pierre.comon@gipsa-lab.grenoble-inp.fr).**FUNDING**

This internship will be funded by the ArtiFicial and Natural Intelligence Toulouse Institute (3IA ANITI), as part of the AI Research **Chair lead by N. Dobigeon.****CONTEXT**

Tensor models are powerful tools for addressing many problems in signal processing, machine learning and beyond [1]–[3]. Yet, their use in these applications typically requires estimating a low-rank tensor from a set of observations corrupted by noise, which is often a difficult task. Moreover, in most cases there is currently no theory for predicting the actual estimation performance that can be attained.

To overcome this gap, in recent years several researchers have studied the asymptotic statistical performance of ideal and practical estimators in the large-dimensional regime,

where the size of the tensor grows large [4]–[6]. In particular, these works have uncovered the abrupt phase transition that the performance of an ideal estimator may undergo as the

signal-to-noise ratio grows (see Figure 1 below for an illustration). While some important advancements have been achieved, many scenarios of practical interest remain unexplored, as well as the practical implications of the existing results in applications.**OBJECTIVES**

The overall goal of this internship is to study extensions and applications of the existing results, as a first step for pushing the existing theory beyond its current limits. We will in particular

consider extensions to more general tensor models that apply to larger classes of realworld problems, including e.g. asymmetric models. Application to practical machine learning problems—such as community detection in hypergraphs [7], latent variable model estimation [2] and high-order co-clustering [8]—will also be considered.

The intern will initially perform computer simulations aimed at understanding the behavior of ideal and practical estimators in the target scenarios/applications. Some theoretical results may then be derived on the basis of these experimental findings. Scientific dissemination of these findings will also be encouraged, via publication of papers and/or participation

in scientific events.

A PhD thesis may be proposed to the intern at the end.

**CANDIDATE PROFILE**

We look for strongly motivated candidates with a solid background on mathematics and statistics, having good programming skills in scientific computing languages (Python, Matlab, Julia). Basic knowledge or interest in random matrix theory is a strong plus.**PRACTICAL INFORMATION**

• The intern will be hosted at the ENSEEIHT site of IRIT, located at 2 rue Charles Camichel,Toulouse.

• The monthly internship gratification is of 600€.

• Application procedure: please send your CV, your report card and a motivation letter to Henrique Goulart

**References**

[1] N. D. Sidiropoulos, L. De Lathauwer, X. Fu, et al., “Tensor decomposition for signal processing and machine

learning,” IEEE Transactions on Signal Processing, vol. 65, no. 13, pp. 3551–3582, 2017.

[2] A. Anandkumar, D. Hsu, S. M. Kakade, et al., “Tensor decompositions for learning latent variable models,”

Journal of Machine Learning Research, vol. 15, pp. 2773–2832, 2014.

[3] S. Rabanser, O. Shchur, and S. Günnemann, “Introduction to tensor decompositions and their applications

in machine learning,” arXiv preprint arXiv:1711.10781, 2017.

[4] A. Jagannath, P. Lopatto, and L. Miolane, “Statistical thresholds for Tensor PCA,” The Annals of Applied Probability,

vol. 30, no. 4, pp. 1910–1933, 2020.

[5] A. Perry, A. S. Wein, and A. S. Bandeira, “Statistical limits of spiked tensor models,” Annales de l’Institut Henri

Poincaré, Probabilités et Statistiques, vol. 56, no. 1, pp. 230–264, 2020.

[6] A. Montanari and E. Richard, “A statistical model for tensor PCA,” Advances in Neural Information Processing

Systems, vol. 4, pp. 2897–2905, 2014. eprint: 1411.1076.

[7] C. Kim, A. S. Bandeira, and M. X. Goemans, “Community detection in hypergraphs, spiked tensor models, and

sum-of-squares,” in 2017 International Conference on Sampling Theory and Applications (SampTA), Tallinn,

Estonia, Jul. 2017, pp. 124–128.

[8] E. E. Papalexakis, N. D. Sidiropoulos, and R. Bro, “From k-means to higher-way co-clustering: Multilinear

decomposition with sparse latent factors,” IEEE Transactions on Signal Processing, vol. 61, no. 2, pp. 493–

506, 2013.

*Master 2 internship proposal – Spring 2021 (5 to 6 months) *

**Contact** : Henrique Goulart

henrique.goulart@irit.fr

#### Design of a multi-robot architecture for patrolling missions

**DESCRIPTION**

This internship aims at designing, developing and testing a distributed software architecture for a Multi-Robot System (MRS), in order to achieve a patrolling mission.

This architecture will be based on two elements:

• a Market-Based Auction (MBA) mechanism for multi-robot task allocation; the tasks to allocate consist in patrol trajectories, observation of points of interest, identification of objects, communication relays, … MBA approaches are based on the following principle: tasks are proposed by an auctioneer, which can be a human operator or a robot of the MRS, and other robots can bid on this task, depending on their capability to achieve it; the auctioneer then decides who wins the auction for each proposed task;

• a Machine Learning (ML) based approach to plan the trajectories of robots; the objective is to learn trajectories from either actual field data or a robot simulator, and to use this function with two objectives: first to compute more precise bids in the MBA approach, and second, to better execute trajectories.

During this internship, the student will then have to develop and test both the MBA and the ML approaches, and to design a global MRS architecture that integrates both. The developments will be evaluated at least on a robotic simulator, and possibly on actual robotic platforms on a small arena available at ONERA.

The student will be integrated within the robotics team at ONERA, among researchers and students working on several projects, robots, and applications.

**APPLICATION PROCEDURE**

Formal applications should include detailed cv, a motivation letter, and transcripts of Bachelor’s degree.

Applications should be sent by email to: advisor emails

*M2 – 4 to 6 month*s

**Contact/Advisor : **Charles Lesire – charles.lesire@onera.fr

#### Representation learning for satellite image

time series classification

**CONTEXT**

In the last years, the advent of Earth observation satellite missions with short revisit time and increased spatial resolution has led to an unprecedented amount of remote sensing images of heterogeneous physical nature (e.g., optical & radar Sentinel time series . . . ) at various scales (e.g., submetric, decametric . . . ). Furthermore, satellite image archives, such as Spot Heritage, are made available by many space agencies. Such massive data extend existing satellite and in-situ acquisition system used to understand, explain and predict the states and trends of our environment.

In order to address challenges raised by such applicative domains, the interdisciplinary institute in artificial intelligence of Toulouse, named the Artificial and Natural Intelligence Toulouse Institute (ANITI) of whom CNES is partner, has proposed to develop innovative

solutions using theoretical advances in core AI scientific areas. The CESBIO lab, with J. Inglada and M. Fauvel, is part of the ANITI Chair entitled “Data-driven approximate Bayesian computation for fusion-based inference from heterogeneous (remote sensing) data” hold by Prof. N.Dobigeon. This chair’s objective is to develop learning algorithms able to extract meaningful information from multi-source, multi-scale and multi-temporal data.

For 4 years now, CESBIO has used machine learning tools to provide automatically the fist land cover map of France from satellite image time series (http://osr-cesbio.ups-tlse. fr/~oso/ and https://www.theia-land.fr/en/ceslist/land-cover-sec/). The master internship is related to the integration of massive multi-source/scale satellite image time series

in learning algorithms for the production of such land use and land cover maps.**OBJECTIVES**

The goal of the internship is to investigate the definition of an auto-encoder architectures adapted to satellite image time series. Such data are structured into three dimensions:

1 spatial, spectral and temporal. Hence, each pixel of a given data cube can be represented as a collection of spectral measurements over the time and spatial domains (see figure 1 for instance).

While several neural architectures have been proposed in the remote sensing literature, most of them have been applied to hyperspectral images of reduced size. Thus, they hardly take into account the temporal dimension and do not scale well w.r.t. the number of pixels.

Therefore, there is a need for specific work in satellite image time-series analysis. The recruited candidate will do a review of auto-encoder architectures used in satellite image times series and will implement the appropriate ones. Tests on large scale data sets will be performed for the classification of land cover types. Depending on the advancement, modification of existing architectures will be considered.

The candidate will be located at the “Maison de la recherche et de la valorisation” close to the CESBIO lab. He/She will be with other master students within the ANITI project. He/She will benefit of a full access to CESBIO and CNES high performance computers.

**CANDIDATE PROFIL**

The candidate must have a solid background in at least one of the following subjects:

- Statistical signal and image processing,
- Machine learning,
- Remote sensing data processing.

A good knowledge of English and scientific programming (Python, C/C++) is required.

**PRACTICAL DETAILS**

- The grant is approximately 620 euros per month.
- Beginning of the internship: February or March 2021, for 6 months.
- To apply, send a CV and a motivation letter to Mathieu Fauvel, mathieu.fauvel@inrae.fr.

*Master internship*

**Contacts** : Matthieu Fauvel (UMR CESBIO, INRAE Toulouse & Jordi Inglada (UMR CESBIO, Cnes Toulouse)

To apply, send a CV and a motivation letter to Mathieu Fauvel, mathieu.fauvel@inrae.fr.

#### Blind inverse problems in microscopy

**TOPIC**

Most of the significant advances in imaging in recent years rely on the use of numerical computation. Examples include super-resolution in microscopy, compressed sensing in magnetic resonance imaging or radar interferometry for earth observation. These techniques

share the prior need to design a mathematical model of the observation system. The acquired data is often described by an equation of the form y = Ax where A is a linear operator that describes the physics of the acquisition. Recovering x then requires inverting the operator. Although these imaging modalities have allowed solving problems beyond reach in the past, their expansion is often severely limited by an important problem: it is impossible to accurately control imaging conditions, resulting in errors on the operator A that make the numerical methods unreliable.*The main objective of this project is to develop theories and algorithms to overcome these difficulties and apply them to microscopy and astronomical imaging.*

This problem is one of the most important current challenges in the field of inverse problems. Depending on the candidate interest, it will be possible to concentrate the efforts on rather theoretical issues or practical issues.**THEORY**

The supervisors have begun investigating various open questions in this field. Two of them will be explored.

Recently [4], Kech and Krahmer provided necessary and sufficient conditions guaranteeing the ability to recover the operator A and the signal x from the measurements y. This implies studying the global injectivity of a bilinear mapping. The setting is however too

restricted for practical applications and we plan to study the local injectivity of the mapping.

A second trail is about the design of optimization algorithms to recover A and x. A standard approach [1] consists in lifting the problem on the space of rank-1 matrices. A traditional approach to solve the resulting problem consists in relaxing the rank 1 constraint by penalizing the nuclear norm. We recently observed that simpler projected gradient descents [3] tend to produce better results. Following [5], we plan to explore the use of continuous relaxations, which discard spurious minimizer and simplify the minimization.

**APPLICATION**

The supervisors of this project have begun a collaboration with the Centre de Biologie Intégrative in Toulouse (CBI), to improve the resolution of microscopes of the imaging facility. In particular, they are interested in the field of Single Molecule Localization Microscopy (SMLM) [2] and Structured Illumination microscopy [6].

The dominant approach to solve the associated inverse problems consists in assuming that the observation operator has been perfectly calibrated before the acquisition. This hypothesis is seldom satisfied and we expect to significantly improve the reconstructions by

using a finer modelling of the system and an identification of the operator. In addition, real improvements of the microscopes might result in new collaborations with the biologists to answer practical problems.

**PRACTICAL ASPECTS**

We are looking for a highly motivated student, willing to continue with a PhD thesis, with a background in electrical engineering (signal/image processing, harmonic analysis) or mathematics (optimization, probability an statistics, geometry). Strong abilities in mathematics or computer sciences will be appreciated. A taste for optics or biological

problems is a plus since applied projects might emerge.

If the candidate is successful, this internship will be pursued by a PhD. Various funding sources will be considered (ADI, FRM, Labex CIMI, doctoral school, ANR, ANITI).

This internship will take place either at IRIT or at INSA (in Toulouse, France), depending on the candidate’s interest. It will be co-supervised by Emmanuel Soubies (CR Toulouse) and Pierre Weiss (CR Toulouse). In addition, the candidate will have access to the CBI (Centre de Biologie Intégrative) with Thomas Mangeat for an access to the microscopy resources and biological problems. Do not hesitate to contact us for more information.**BIBLIOGRAPHY**

[1] Ali Ahmed, Benjamin Recht, and Justin Romberg. Blind deconvolution using convex programming. IEEE Transactions on Information Theory, 60(3):1711–1732, 2013.

[2] Valentin Debarnot, Paul Escande, Thomas Mangeat, and Pierre Weiss. Learning low- dimensional models of microscopes. IEEE Transactions on Computational Imaging, 2020.

[3] Valentin Debarnot and Weiss Pierre. Blind inverse problems with isolated spikes. ArXiv, 2020.

[4] Michael Kech and Felix Krahmer. Optimal injectivity conditions for bilinear inverse problems with applications to identifiability of deconvolution problems. SIAM Journal on Applied Algebra and Geometry, 1(1):20–37, 2017.

[5] Emmanuel Soubies, Laure Blanc-Féraud, and Gilles Aubert. A continuous exact \ell_0 penalty (cel0) for least squares regularized problem. SIAM Journal on Imaging Sciences, 8(3):1607–1639, 2015.

[6] Emmanuel Soubies and Michael Unser. Computational super-sectioning for single-slice structuredillumination microscopy. IEEE Transactions on Computational Imaging, 5(2):240–250, 2018.

**APPLICATION PROCEDURE**

Formal applications should include detailed cv, a motivation letter, and transcripts of Bachelor’s degree.**Applications should be sent by email to: advisor emails**

*Master 2 – 5 to 6 months*

**Contacts** : Emmanuel Soubies – emmanuel.soubies@irit.fr & Pierre Weiss – Pierre.armand.weiss@gmail.com