SOUBIES , Emmanuel

This thesis is devoted to two problems encountered in signal and image processing. The first oneconcerns the 3D reconstruction of biological structures from multi-angle total interval reflectionfluorescence microscopy (MA-TIRF). Within this context, we propose to tackle the inverse problem byusing a variational approach and we analyze the...

We propose an algorithm to segment 2D ellipses or 3D ellipsoids. This problem is of fundamental importance in various applications of cell biology. The algorithm consists of minimizing a contrast invariant energy defined on sets of non overlapping ellipsoids. This highly non convex problem is solved by combining a stochastic approach based on...

We propose a new class of exact continuous relaxations of l0-regularized criteria involving non-quadratic data terms such as the Kullback-Leibler divergence and the logistic regression, possibly combined with an l2 regularization. We first prove the existence of global minimizers for such problems and characterize their local minimizers.Then,...

The resolution of optimization problems involving the ℓ0 pseudo-norm has proven to be of importance in signal processing and machine learning applications for selecting relevant variables. Among the vast class of existing approaches dealing with the intrinsic NP-hardness of such problems, continuous (possibly non-convex) relaxations have been...

For more than two decades, several continuous (and generally separable) penalties approximating (relaxing) the l0-pseudo norm have been proposed. Although some "good" properties for such penalties have been highlighted, the choice of one relaxation rather than another one remains unclear. One approach to compare them is to investigate their...

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...

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...

The l2-l0 optimization problem has been widely studied because of its importance in many applications in signal and image processing. In this paper, we focus on the Iterative Hard Thresholding (IHT) algorithm which minimizes directly the l2-l0 criterion, without approximating the l0 pseudo-norm, and converges to a (local) minimizer. Within this...

Numerous nonconvex continuous penalties have been proposed to approach the l0 pseudo-norm for optimization purpose. Apart from the theoretical results for convex l1 relaxation under restrictive hypothesis, only few works have been devoted to analyze the consistency, in terms of minimizers, between the l0-regularized least square functional and...

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...

Within the framework of the l0 regularized least squares problem, we focus, in this paper, on nonconvex continuous penalties approximating the l0 -norm. Such penalties are known to better promote sparsity than the l1 convex relaxation. Based on some results in one dimension and in the case of orthogonal matrices, we propose the Continuous Exact...

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...

This paper is devoted to the analysis of necessary (not sufficient) optimality conditions for the l0-regularized least-squares minimization problem. Such conditions are the roots of the plethora of algorithms that have been designed to cope with this NP-hard problem. Indeed, as global optimality is, in general, intractable, these algorithms...

Single molecule localization microscopy has made great improvements in spatial resolution achieving performance beyond the diffraction limit by sequentially activating and imaging small subsets of molecules. Here, we present an algorithm designed for high-density molecule localization which is of a major importance in order to improve the...

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...

In this paper we address the problem of cells detection from mi-croscopy images. We construct a dictionary of candidate shapes obtained from previous segmentation maps and define an energy function to select the best candidates. The energy minimization is performed by an iterative graph cut algorithm. The proposed approach optimally combines...

We propose a new model for the reconstruction of biological struc- tures using Multiple-Angle Total Internal Reflection Fluorescence Microscopy (MA-TIRFM). This recent microscopy technique allows the visualization of sub-cellular structures around the plasma mem- brane which is of fundamental importance in the comprehension of exchanges...

Super-resolution microscopy techniques allow to overstep the diffraction limit of conventional optics. Theses techniques are very promising since they give access to the visualisation of finer structures which is of fundamental importance in biology. In this paper we deal with Multiple-Angle Total Internal Reflection Mi- croscopy (MA-TIRFM)...

We propose a new model for the reconstruction of biological struc- tures using Multiple-Angle Total Internal Reflection Fluorescence Microscopy (MA-TIRFM). This recent microscopy technique allows the visualization of sub-cellular structures around the plasma mem- brane which is of fundamental importance in the comprehension of exchanges...

On-grid based direction-of-arrival (DOA) estimation methods rely on the resolution of a difficult group-sparse optimization problem that involves the l20 pseudo-norm. In this work, we show that an exact relaxation of this problem can be obtained by replacing the l20 term with a group minimax concave penalty with suitable parameters. This...

Total internal reflection fluorescence microscopy (TIRF) produces 2D images of the fluorescent activity integrated over a very thin layer adjacent to the glass coverslip. By varying the illumination angle (multi-angle TIRF), a stack of 2D images is acquired from which it is possible to estimate the axial position of the observed biological...

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...

High resolution imaging of molecules at the cell-substrate interface is required for understanding key biological processes. Here we propose a complete pipeline for multi-angle total internal reflection fluorescence microscopy (MA-TIRF) going from instrument design and calibration procedures to numerical reconstruction. Our custom setup is...

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.