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2. Surpassing light inhomogeneities in structured‐illumination microscopy with FlexSIM.

Author

Soubies, Emmanuel, Nogueron, Alejandro, Pelletier, Florence, Mangeat, Thomas, Leterrier, Christophe, Unser, Michael, and Sage, Daniel

Subjects
*IMAGE reconstruction, *MICROSCOPY, *FLUORESCENCE, *NOISE
Abstract

Super‐resolution structured‐illumination microscopy (SIM) is a powerful technique that allows one to surpass the diffraction limit by up to a factor two. Yet, its practical use is hampered by its sensitivity to imaging conditions which makes it prone to reconstruction artefacts. In this work, we present FlexSIM, a flexible SIM reconstruction method capable to handle highly challenging data. Specifically, we demonstrate the ability of FlexSIM to deal with the distortion of patterns, the high level of noise encountered in live imaging, as well as out‐of‐focus fluorescence. Moreover, we show that FlexSIM achieves state‐of‐the‐art performance over a variety of open SIM datasets. [ABSTRACT FROM AUTHOR]

Published
2024
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5. The MLE is a reliable source: sharp performance guarantees for localization problems

Author

Munier, Nathanaël, Soubies, Emmanuel, Weiss, Pierre, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Centre de Biologie Intégrative (CBI), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), ANR-21-CE48-0008,MICROBLIND,Problèmes inverses aveugles et microscopie optique(2021), ANR-11-LABX-0040,CIMI,Centre International de Mathématiques et d'Informatique (de Toulouse)(2011), Munier, Nathanaël, Problèmes inverses aveugles et microscopie optique - - MICROBLIND2021 - ANR-21-CE48-0008 - AAPG2021 - VALID, and Centre International de Mathématiques et d'Informatique (de Toulouse) - - CIMI2011 - ANR-11-LABX-0040 - LABX - VALID

Subjects
[MATH.MATH-PR]Mathematics [math]/Probability [math.PR], [STAT]Statistics [stat], [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], [INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV], [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, [STAT] Statistics [stat], [SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing
Abstract

28 pages; Single source localization from low-pass filtered measurements is ubiquitous in optics, wireless communications and sound processing. We analyse the performance of the maximum likelihood estimator (MLE) in this context with additive white Gaussian noise. We derive necessary conditions and sufficient conditions on the maximum admissible noise level to reach a given precision with high probability. The two conditions match closely, with a discrepancy related to the conditioning of a noiseless cost function. They tightly surround the Cramér-Rao lower bound for low noise levels. However, they are significantly more precise for larger levels. An outcome is new optimization criteria for the design of point spread functions in single molecule microscopy.

Published
2022

6. Accelerating Non-Negative and Bounded-Variable Linear Regression Algorithms with Safe Screening

Author

Dantas, Cassio F., Soubies, Emmanuel, Févotte, Cédric, Institut Montpelliérain Alexander Grothendieck (IMAG), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Centre National de la Recherche Scientifique (CNRS), European Project: 6681839, Territoires, Environnement, Télédétection et Information Spatiale (UMR TETIS), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-AgroParisTech-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), and Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)

Subjects
FOS: Computer and information sciences, Computer Science - Machine Learning, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, Machine Learning (stat.ML), Machine Learning (cs.LG)
Abstract

Non-negative and bounded-variable linear regression problems arise in a variety of applications in machine learning and signal processing. In this paper, we propose a technique to accelerate existing solvers for these problems by identifying saturated coordinates in the course of iterations. This is akin to safe screening techniques previously proposed for sparsity-regularized regression problems. The proposed strategy is provably safe as it provides theoretical guarantees that the identified coordinates are indeed saturated in the optimal solution. Experimental results on synthetic and real data show compelling accelerations for both non-negative and bounded-variable problems.

Published
2022

7. On the Relationships between Transform-Learning NMF and Joint-Diagonalization

Author

Zhang, Sixin, Soubies, Emmanuel, Févotte, Cédric, Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, and European Project: CoG-6681839,ERC FACTORY

Subjects
[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [INFO]Computer Science [cs]
Abstract

Non-negative matrix factorization with transform learning (TL-NMF) is a recent idea that aims at learning data representations suited to NMF. In this work, we relate TL-NMF to the classical matrix joint-diagonalization (JD) problem. We show that, when the number of data realizations is sufficiently large, TL-NMF can be replaced by a two-step approach -- termed as JD+NMF -- that estimates the transform through JD, prior to NMF computation. In contrast, we found that when the number of data realizations is limited, not only is JD+NMF no longer equivalent to TL-NMF, but the inherent low-rank constraint of TL-NMF turns out to be an essential ingredient to learn meaningful transforms for NMF.

Published
2021

8. User-friendly Building of Reconstruction Algorithms with GlobalBioIm

Author

Donati, Laurène, Soubies, Emmanuel, Unser, Michael, Soubies, Emmanuel, Biomedical Imaging Group [Lausanne], Ecole Polytechnique Fédérale de Lausanne (EPFL), Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique (CNRS), and DAS-SAB

Subjects
[INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV], [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV]
Abstract

International audience; The current shift towards computational imaging has made reconstruction procedures an integral part of many advanced imaging systems. A consequence is that imaging scientists now commonly require efficient and reliable computational tools for solving their inverse problems. To this end, we recently developed GlobalBioIm, an open-source Matlab library that standardizes the resolution of a wide range of imaging problems [1]. This toolbox gives access to cutting-edge reconstruction algorithms, and can be extended to new modalities and methods by combining elementary modules. The versatility and efficiency of GlobalBioIm have been highlighted in a series of recent high-impact works [2-4]. Driven by these encouraging applications, we have devoted our efforts towards improving the usability of GlobalBioIm by those with limited expertise in inverse problems and optimization theory. The outcome is a new user-friendly Matlab interface (Figure 1) that allows non-experts to intuitively build tailored reconstruction algorithms with minimal effort. Figure 1: The new GlobalBioIm GUI (left) can be used to solve various inverse problems (right).

Published
2020

9. Inner-Loop Free ADMM for Cryo-EM

Author

Donati, Lauréne, Soubies, Emmanuel, Unser, Michael, Biomedical Imaging Group [Lausanne], Ecole Polytechnique Fédérale de Lausanne (EPFL), and Soubies, Emmanuel

Subjects
regularization, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV], Cryo-EM reconstruction, splitting, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], inverse problem, inner-loop-free, convergence speed, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, alternating-direction of multipliers method (ADMM), [SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing
Abstract

International audience; Thanks to recent advances in signal processing, the interest for fast l1-regularized reconstruction algorithms in cryo-electron mi-croscopy (cryo-EM) has intensified. The approaches based on the alternating-direction of multipliers method (ADMM) are particularly well-suited due to the prime convergence speed and flexibility of use of this algorithm. Yet, the standard ADMM scheme still relies on a nested conjugate gradient (CG) to solve the linear step in its alternating-minimization procedure, which can be costly when handling large-scale problems. In this work, we present an inner-loop-free ADMM algorithm for 3D reconstruction in cryo-EM. By using an appropriate splitting scheme, we are able to avoid the use of CG for solving the linear step. This leads to a substantial increase in algorithmic speed, as demonstrated by our experiments.

Published
2019

10. Expanding boundaries of Gap Safe screening

Author

Cássio Dantas, Soubies, Emmanuel, Fevotte, Cedric, Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique (CNRS), ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), European Project: 681839,H2020,ERC-2015-CoG,FACTORY(2016), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
Signal Processing (eess.SP), FOS: Computer and information sciences, Computer Science - Machine Learning, non-negativity, sparse regression, Machine Learning (cs.LG), Convex optimization, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Optimization and Control (math.OC), FOS: Electrical engineering, electronic engineering, information engineering, FOS: Mathematics, safe screening rules, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Electrical Engineering and Systems Science - Signal Processing, Mathematics - Optimization and Control, beta-divergence
Abstract

International audience; Sparse optimization problems are ubiquitous in many fields such as statistics, signal/image processing and machine learning. This has led to the birth of many iterative algorithms to solve them. A powerful strategy to boost the performance of these algorithms is known as safe screening: it allows the early identification of zero coordinates in the solution, which can then be eliminated to reduce the problem's size and accelerate convergence. In this work, we extend the existing Gap Safe screening framework by relaxing the global strong-concavity assumption on the dual cost function. Instead, we exploit local regularity properties, that is, strong concavity on well-chosen subsets of the domain. The non-negativity constraint is also integrated to the existing framework. Besides making safe screening possible to a broader class of functions that includes beta-divergences (e.g., the Kullback-Leibler divergence), the proposed approach also improves upon the existing Gap Safe screening rules on previously applicable cases (e.g., logistic regression). The proposed general framework is exemplified by some notable particular cases: logistic function, beta = 1.5 and Kullback-Leibler divergences. Finally, we showcase the effectiveness of the proposed screening rules with different solvers (coordinate descent, multiplicative-update and proximal gradient algorithms) and different data sets (binary classification, hyperspectral and count data).

Published
2021

11. The Sliding Frank-Wolfe Algorithm for the BLASSO

Author

Denoyelle, Quentin, Duval, Vincent, Peyré, Gabriel, Soubies, Emmanuel, Biomedical Imaging Group [Lausanne], Ecole Polytechnique Fédérale de Lausanne (EPFL), Laboratoire Traitement et Communication de l'Information (LTCI), Télécom ParisTech-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales (MOKAPLAN), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Département de Mathématiques et Applications - ENS Paris (DMA), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique (CNRS), CNRS, Grélaud, Françoise, CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), École normale supérieure - Paris (ENS-PSL), Université Toulouse Capitole (UT Capitole), Université Fédérale Toulouse Midi-Pyrénées-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Inria de Paris, and Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)

Subjects
[INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, Traitement du signal et de l'image, [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG]
Abstract

International audience; This paper showcases the theoretical and numerical performance of the Sliding Frank-Wolfe, which is a novel optimization algorithm to solve the BLASSO sparse spikes super-resolution problem. The BLASSO is a continuous (i.e. off-the-grid or grid-less) counterpart to the well-known 1 sparse regularisation method (also known as LASSO or Basis Pursuit). Our algorithm is a variation on the classical Frank-Wolfe (also known as conditional gradient) which follows a recent trend of interleaving convex optimization updates (corresponding to adding new spikes) with non-convex optimization steps (corresponding to moving the spikes). Our main theoretical result is that this algorithm terminates in a finite number of steps under a mild non-degeneracy hypothesis. We then target applications of this method to several instances of single molecule fluorescence imaging modalities, among which certain approaches rely heavily on the inversion of a Laplace transform. Our second theoretical contribution is the proof of the exact support recovery property of the BLASSO to invert the 1-D Laplace transform in the case of positive spikes. On the numerical side, we conclude this paper with an extensive study of the practical performance of the Sliding Frank-Wolfe on different instantiations of single molecule fluorescence imaging, including convolutive and non-convolutive (Laplace-like) operators. This shows the versatility and superiority of this method with respect to alternative sparse recovery technics.

Published
2019

12. On the Local Minimizers of the CEL0 Relaxation

Author

Soubies, Emmanuel, Blanc-Féraud, Laure, Aubert, Gilles, Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Centre National de la Recherche Scientifique (CNRS), Morphologie et Images (MORPHEME), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Biologie Valrose (IBV), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Signal, Images et Systèmes (Laboratoire I3S - SIS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (LJAD), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), ANR-19-P3IA-0002,3IA@cote d'azur,3IA Côte d'Azur(2019), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Signal, Images et Systèmes (Laboratoire I3S - SIS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)

Subjects
[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

International audience; We study the strict local minimizers of the CEL0 func-tional, an exact continuous relaxation of the`0-regularized least-squarescriterion. More precisely, we derive a necessary and sufficient conditionfor strict local optimality, recalling that global minimizers are strict.Moreover, we quantify the number of strict local (not global) minimizersof the initial functional that are eliminated by the relax.

Published
2019

13. CEL0: a continuous alternative to l0 penalty

Author

Soubies, Emmanuel, Blanc-Féraud, Laure, Aubert, Gilles, Morphologie et Images (MORPHEME), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Biologie Valrose (IBV), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Signal, Images et Systèmes (Laboratoire I3S - SIS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Soubies, Emmanuel, Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Signal, Images et Systèmes (Laboratoire I3S - SIS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and Laboratoire Jean Alexandre Dieudonné (LJAD)

Subjects
minimizer equivalence, [INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, CEL0 penalty, inverse problems, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], sparse modeling, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, [SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing, l0 regularisation
Abstract

International audience; This paper presents a new way to address the NP-hard combinatorial l2-l0 problem by minimizing a continuous relaxed functional preserving the minimizers of the initial energy. We propose the Continuous Exact l0 penalty (CEL0), an approximation of the l0 norm leading to a tight continuous relaxation of the l2-l0 criteria whose global minimizers contain those of the l0 penalized least-squares functional. Links between local minimizers of these two functionals are also investigated. This short communication summarizes the main results of our recent work [1].

Published
2015

14. Expanding Boundaries of Gap Safe Screening.

Author

Dantas, Cassio F., Soubies, Emmanuel, and Févotte, Cédric

Subjects
*BOOSTING algorithms, *IMAGE processing, *COST functions, *MACHINE learning, *LOGISTIC regression analysis
Abstract

Sparse optimization problems are ubiquitous in many fields such as statistics, signal/image processing and machine learning. This has led to the birth of many iterative algorithms to solve them. A powerful strategy to boost the performance of these algorithms is known as safe screening: it allows the early identification of zero coordinates in the solution, which can then be eliminated to reduce the problem's size and accelerate convergence. In this work, we extend the existing Gap Safe screening framework by relaxing the global strong-concavity assumption on the dual cost function. Instead, we exploit local regularity properties, that is, strong concavity on well-chosen subsets of the domain. The non-negativity constraint is also integrated to the existing framework. Besides making safe screening possible to a broader class of functions that includes fi-divergences (e.g., the Kullback-Leibler divergence), the proposed approach also improves upon the existing Gap Safe screening rules on previously applicable cases (e.g., logistic regression). The proposed general framework is exemplified by some notable particular cases: logistic function, fi= 1:5 and Kullback-Leibler divergences. Finally, we showcase the effectiveness of the proposed screening rules with different solvers (coordinate descent, multiplicative-update and proximal gradient algorithms) and different data sets (binary classification, hyperspectral and count data). [ABSTRACT FROM AUTHOR]

Published
2021

15. Direction-of-Arrival Estimation Through Exact Continuous ℓ2,0-Norm Relaxation.

Author

Soubies, Emmanuel, Chinatto, Adilson, Larzabal, Pascal, Romano, Joao M. T., and Blanc-Feraud, Laure

Subjects
MATHEMATICAL optimization, SPARSE matrices, ANTENNA arrays, COMPUTER simulation, SIGNAL processing
Abstract

On-grid based direction-of-arrival (DOA) estimation methods rely on the resolution of a difficult group-sparse optimization problem that involves the ℓ2,0 pseudo-norm. In this work, we show that an exact relaxation of this problem can be obtained by replacing the ℓ2,0 term with a group minimax concave penalty with suitable parameters. This relaxation is more amenable to non-convex optimization algorithms as it is continuous and admits less local (not global) minimizers than the initial ℓ2,0-regularized criteria. We then show on numerical simulations that the minimization of the proposed relaxation with an iteratively reweighted ℓ2,1 algorithm leads to an improved performance over traditional approaches. [ABSTRACT FROM AUTHOR]

Published
2021
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16. Joint Angular Refinement and Reconstruction for Single-Particle Cryo-EM.

Author

Zehni, Mona, Donati, Laurene, Soubies, Emmanuel, Zhao, Zhizhen, and Unser, Michael

Subjects
ELECTRON microscopy, MICROSCOPY, DENSITY, ANGLES
Abstract

Single-particle cryo-electron microscopy (cryo-EM) reconstructs the three-dimensional (3D) structure of bio-molecules from a large set of 2D projection images with random and unknown orientations. A crucial step in the single-particle cryo-EM pipeline is 3D refinement, which resolves a high-resolution 3D structure from an initial approximate volume by refining the estimation of the orientation of each projection. In this work, we propose a new approach that refines the projection angles on the continuum. We formulate the optimization problem over the density map and the orientations jointly. The density map is updated using the efficient alternating-direction method of multipliers, while the orientations are updated through a semi-coordinate-wise gradient descent for which we provide an explicit derivation of the gradient. Our method eliminates the requirement for a fine discretization of the orientation space and does away with the classical but computationally expensive template-matching step. Numerical results demonstrate the feasibility and performance of our approach compared to several baselines. [ABSTRACT FROM AUTHOR]

Published
2020
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17. Some results on sparse L2-L0 reconstruction: Continuous Exact L0 penalties

Author

Blanc-Féraud, Laure, Soubies, Emmanuel, Aubert, Gilles, Morphologie et Images (MORPHEME), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Biologie Valrose (IBV), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Signal, Images et Systèmes (Laboratoire I3S - SIS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (LJAD), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), GdR MaDICS, ENS Cachan, Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Signal, Images et Systèmes (Laboratoire I3S - SIS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), and Blanc-Féraud, Laure

Subjects
[INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV], [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV]
Abstract

International audience; A smooth exact approximation of functional L2-L0 (least squares functional with sparse penalizing term using a L0 norm) is presented. This functional, named CEL0 for Continuous Exact L0 approximation is said exact as it preserves global minimizers and remove some of the local minimizers of the L2-L0 functional. More general results on smooth approximation of the L2-L0 functional are also given, describing a class of continuous functions with the properties of preservation of minimizers as described above. Simulation results are presented.

Published
2016

18. ERRATUM: A Continuous Exact l0 penalty (CEL0) for least squares regularized problem

Author

Soubies, Emmanuel, Blanc-Féraud, Laure, Aubert, Gilles, Morphologie et Images (MORPHEME), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Biologie Valrose (IBV), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Signal, Images et Systèmes (Laboratoire I3S - SIS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (JAD), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Signal, Images et Systèmes (Laboratoire I3S - SIS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS)

Subjects
local minimizers, underdetermined linear systems, 021103 operations research, global minimizers, minimizers equivalence, inverse problems, Applied Mathematics, General Mathematics, 0211 other engineering and technologies, 02 engineering and technology, nonconvex nonsmooth penalty, sparse modelling, l0 regularization, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Continuous Exact l0 penalty
Abstract

International audience; Lemma 4.4 in [E. Soubies, L. Blanc-Féraud and G. Aubert, SIAM J. Imaging Sci., 8 (2015), pp. 1607-1639] is wrong for local minimizers of the CEL0 functional. The argument used to conclude the proof of this lemma is not sufficient in the case of local minimizers. In this note, we supplya revision of this Lemma where new results are established for local minimizers. Theorem 4.8 in that paper remains unchanged but the proof has to be rewritten according to the new version of the lemma. Finally, some remarks of this paper are also rewritten using the corrected lemma.

Published
2016
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19. A UNIFIED VIEW OF EXACT CONTINUOUS PENALTIES FOR ℓ2-ℓ0 MINIMIZATION.

Author

SOUBIES, EMMANUEL, BLANC-FÉRAUD, LAURE, and AUBERT, GILLES

Subjects
*LEAST squares, *MATHEMATICAL reformulation, *LINEAR systems, *MATHEMATICAL equivalence, *MATHEMATICAL optimization, *APPROXIMATION theory
Abstract

Numerous nonconvex continuous penalties have been proposed to approach the ℓ0 pseudonorm for optimization purpose. Apart from the theoretical results for convex ℓ1 relaxation under restrictive hypotheses, only few works have been devoted to analyze the consistency, in terms of minimizers, between the ℓ0-regularized least squares functional and relaxed ones using continuous approximations. In this context, two questions are of fundamental importance: do relaxed functionals preserve global minimizers of the initial one? Do these approximations introduce unwanted new (local) minimizers? In this paper we answer these questions by deriving necessary and sufficient conditions on such ℓ0 continuous approximations in order that each (local and global) minimizer of the underlying relaxation is also a minimizer of the ℓ2-ℓ0 functional and that all the global minimizers of the initial functional are preserved. Hence, a general class of penalties is provided giving a unified view of exact continuous approximations of the ℓ0-norm within the ℓ2-ℓ0 minimization framework. As the inferior limit of this class of penalties, we get the recently proposed continuous exact ℓ0 penalty. Finally, state of the art penalties, such as minimax concave penalty, smoothly clipped absolute deviation, or capped-ℓ1, are analyzed according to the proposed class of exact continuous penalties. [ABSTRACT FROM AUTHOR]

Published
2017
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24. Dictionary Learning with Statistical Sparsity in the Presence of Noise

Author

Michael Unser, Emmanuel Soubies, Shayan Aziznejad, Biomedical Imaging Group [Lausanne], Ecole Polytechnique Fédérale de Lausanne (EPFL), Signal et Communications (IRIT-SC), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Centre National de la Recherche Scientifique (CNRS), Swiss National Science Foundation under Grant 200020184646 / 1, European Research Council (ERC) through the European Union’s Horizon 2020 Research and Innovation Programme under Grant 692726-GlobalBioIm, and Soubies, Emmanuel

Subjects
Noise measurement, Computer science, Stochastic process, sparse coding, 020206 networking & telecommunications, Dictionary learning, 02 engineering and technology, Sparse approximation, 16. Peace & justice, Stable distribution, Set (abstract data type), stable distribution, Robustness (computer science), 0202 electrical engineering, electronic engineering, information engineering, empirical characteristic function, 020201 artificial intelligence & image processing, Noise (video), Neural coding, sparse representation, Algorithm, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, [SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing
Abstract

International audience; We consider a new stochastic formulation of sparse representations that is based on the family of symmetric α-stable (SαS) distributions. Within this framework, we develop a novel dictionary-learning algorithm that involves a new estimation technique based on the empirical characteristic function. It finds the unknown parameters of an SαS law from a set of its noisy samples. We assess the robustness of our algorithm with numerical examples.

Published
2021

25. A Framework for Multi-angle Tirf Microscope Calibration

Author

Gilles Aubert, Emmanuel Soubies, Sébastien Schaub, Agata Radwanska, Laure Blanc-Féraud, Ellen Van Obberghen-Schilling, Morphologie et Images (MORPHEME), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Biologie Valrose (IBV), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Signal, Images et Systèmes (Laboratoire I3S - SIS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Institut de Biologie Valrose (IBV), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (JAD), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Soubies, Emmanuel, Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Signal, Images et Systèmes (Laboratoire I3S - SIS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)

Subjects
0301 basic medicine, Fluorescence-lifetime imaging microscopy, Microscope, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, Computer science, Pipeline (computing), ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Iterative reconstruction, Multi-Angle TIRF microscopy, 01 natural sciences, Imaging phantom, law.invention, 010309 optics, 03 medical and health sciences, fluorescence imaging, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, law, 0103 physical sciences, Calibration, Computer vision, ComputingMethodologies_COMPUTERGRAPHICS, microscope calibration, business.industry, 3D reconstruction, image reconstruction, Lens (optics), 030104 developmental biology, [INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV], [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], Artificial intelligence, business
Abstract

International audience; This communication presents a pipeline for Multi-Angle TIRF calibration from the measurement of the incident angle to the model validation. This problem is of major importance when dealing with 3D reconstruction methods from a set of MA-TIRF acquisitions since the reconstruction accuracy highly depends on the agreement between the theoretical model and the physical system. One main issue is then to build phantom samples with known geometry, or known properties, in order to adjust and/or validate the model. This paper describes such a calibration procedure using a lens as phantom sample and proposes a new model validation experiment based on a dual-color co-localization.

Published
2016
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26. L0-Optimization for Channel and DOA Sparse Estimation

Author

Adilson Chinatto, Laure Blanc-Féraud, Jean-Pierre Barbot, Emmanuel Soubies, Cynthia Junqueira, João Marcos Travassos Romano, Pascal Larzabal, Soubies, Emmanuel, Laboratory of Signal Processing for Communications (DSPCom), Universidade Estadual de Campinas = University of Campinas (UNICAMP), Morphologie et Images (MORPHEME), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut de Biologie Valrose (IBV), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Signal, Images et Systèmes (Laboratoire I3S - SIS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Systèmes et Applications des Technologies de l'Information et de l'Energie (SATIE), École normale supérieure - Cachan (ENS Cachan)-Université Paris-Sud - Paris 11 (UP11)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-École normale supérieure - Rennes (ENS Rennes)-Université de Cergy Pontoise (UCP), Université Paris-Seine-Université Paris-Seine-Conservatoire National des Arts et Métiers [CNAM] (CNAM), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-Centre National de la Recherche Scientifique (CNRS), University of Campinas [Campinas] (UNICAMP), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), Université Paris-Seine-Université Paris-Seine-Conservatoire National des Arts et Métiers [CNAM] (CNAM)-Centre National de la Recherche Scientifique (CNRS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Nice Sophia Antipolis (... - 2019) (UNS), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Signal, Images et Systèmes (Laboratoire I3S - SIS)

Subjects
Estimation, Mathematical optimization, Channel (digital image), [INFO.INFO-NI] Computer Science [cs]/Networking and Internet Architecture [cs.NI], Computer science, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, Matching pursuit algorithms, Array processing, Sparse approximation, [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI], [INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV], [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], Minification, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Sparse matrix, [SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing
Abstract

International audience; This paper is devoted to two classical sparse problems in array processing: Channel estimation and DOA estimation. It is shown after some background and some recent results in l0 optimization how this latter can be used, at the same computational cost, in order to obtain improvement in comparison with l1 optimization for sparse estimation.

Published
2015
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27. Closed-Form Expression Of The Fourier Ring-Correlation For Single-Molecule Localization Microscopy

Author

Michael Unser, Daniel Sage, Emmanuel Soubies, Thanh-an Pham, Biomedical Imaging Group [Lausanne], Ecole Polytechnique Fédérale de Lausanne (EPFL), and Soubies, Emmanuel

Subjects
[SPI.OPTI] Engineering Sciences [physics]/Optics / Photonic, [INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing, Fourier-ring correlation, 02 engineering and technology, 03 medical and health sciences, symbols.namesake, Sampling (signal processing), [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Point (geometry), Image resolution, 030304 developmental biology, [SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing, Physics, 0303 health sciences, Resolution (electron density), Estimator, 021001 nanoscience & nanotechnology, Fourier transform, Kernel (image processing), [INFO.INFO-TI] Computer Science [cs]/Image Processing [eess.IV], [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], symbols, [SPI.OPTI]Engineering Sciences [physics]/Optics / Photonic, Closed-form expression, 0210 nano-technology, Single-molecule localization microscopy, Algorithm, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, image resolution
Abstract

International audience; Single-molecule localization microscopy (SMLM) is a popular microscopic technique that achieves super resolution imaging by localizing individual blinking molecules in thousands of frames. Therefore , the reconstructed high-resolution image is a combination of millions of point sources. This particular computational reconstruction leads to the question of the estimation of the image resolution. Fourier-ring correlation (FRC) is the standard tool for assessing the resolution. It has been proposed for SMLM by computing a discrete correlation in the Fourier domain. In this work, we derive a closed-form expression to compute the continuous FRC. Our implementation provides an exact FRC and an alternative to compute a parameter-free FRC. In addition, it gives insights on the discrepancy of the discrete FRC and yields a rule to select its parameters such as the spatial sampling step or the width of the kernel used as density estimator.

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28. Nonlinear Inverse Problems in Quantitative Phase Imaging

Author

Pham, Thanh-An Michel, Unser, Michaël, and Soubies, Emmanuel Emilien Louis

Subjects
optical diffraction tomography, Quantitative phase imaging, Lippmann-Schwinger equation, nonlinear inverse problem, computational microscopy, single-molecule localization microscopy
Abstract

The topic of this thesis is the development of new algorithmic reconstruction methods for quantitative phase imaging (QPI). In the past decade, advanced QPI has emerged as a valuable tool to study label-free biological samples and uncover their 3D structural information. This unique tool takes advantage of the scattering of light that results from the complex interplay between the incident electromagnetic wave and the specimen of interest. Yet, the reconstruction process presents numerous challenges in part due to the nonlinear nature of light scattering. In this thesis, we investigate an accurate nonlinear wave-propagation model that relies on the Lippmann-Schwinger (LiSc) equation and apply it to 3D QPI within a variational framework. Our first contribution is a proper discretization of LiSc and a computationally efficient implementation of the nonlinear model. Using our novel forward model, we formulate an inverse-scattering problem within a modern variational framework and solve it to recover the 3D refractive-index (RI) map of a sample when the measurements are complex-valued. In such a setting, the sample is probed with a series of tilted incident waves, while the complex-valued waves are recorded for each illumination. Our algorithmic reconstruction involves a nontrivial proximal gradient-based iterative scheme that requires the Jacobian matrix of the nonlinear operator, for which we are able to derive an explicit expression. By accounting for multiple scattering and adding suitable prior knowledge, our results show that we significantly improve the quality of reconstruction over the state of the art. We then adapt our LiSc model to intensity-only measurements, which has the advantage of simplifying the acquisition setup. We solve this harder inverse problem by leveraging recent advances in proximal algorithms. Our method obtains RI maps with a quality similar to that obtained from complex measurements. Finally, we propose an extension of single-molecule localization microscopy. This modality delivers nanoscale resolution by sequentially activating a subset of fluorescent labels and by extracting their superresolved position. The emission patterns of each label can be distorted by the sample, which reduces the localization accuracy if not accounted for. Here, we exploit those sample-induced aberrations to recover the RI map. We propose an optimization framework in which we reconstruct the RI map using LiSc and optimize the label positions in a joint fashion. Our results show that we effectively recover the RI map of the sample and further improve the localization.

29. Versatile reconstruction framework for diffraction tomography with intensity measurements and multiple scattering.

Author

Pham TA, Soubies E, Goy A, Lim J, Soulez F, Psaltis D, and Unser M

Abstract

Taking benefit from recent advances in both phase retrieval and estimation of refractive indices from holographic measurements, we propose a unified framework to reconstruct them from intensity-only measurements. Our method relies on a generic and versatile formulation of the inverse problem and includes sparsity constraints. Its modularity enables the use of a variety of forward models, from simple linear ones to more sophisticated nonlinear ones, as well as various regularizers. We present reconstructions that deploy either the beam-propagation method or the iterative Lippmann-Schwinger model, combined with total-variation regularization. They suggest that our proposed (intensity-only) method can reach the same performance as reconstructions from holographic (complex) data. This is of particular interest from a practical point of view because it allows one to simplify the acquisition setup.

Published
2018
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30. Efficient inversion of multiple-scattering model for optical diffraction tomography.

Author

Soubies E, Pham TA, and Unser M

Abstract

Optical diffraction tomography relies on solving an inverse scattering problem governed by the wave equation. Classical reconstruction algorithms are based on linear approximations of the forward model (Born or Rytov), which limits their applicability to thin samples with low refractive-index contrasts. More recent works have shown the benefit of adopting nonlinear models. They account for multiple scattering and reflections, improving the quality of reconstruction. To reduce the complexity and memory requirements of these methods, we derive an explicit formula for the Jacobian matrix of the nonlinear Lippmann-Schwinger model which lends itself to an efficient evaluation of the gradient of the data-fidelity term. This allows us to deploy efficient methods to solve the corresponding inverse problem subject to sparsity constraints.

Published
2017
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