Assistant professor

École Centrale de Nantes (ECN) /
Laboratoire des Sciences du Numérique de Nantes (LS2N)

Research Team SIMS (Signal, Image and Sound)

Office S-207

Phone (33) 2 40 37 69 15

Sebastien * dot * Bourguignon * at * ec-nantes.fr

This project lies at the interface between signal processing and operations research. It aims to propose new optimization strategies based on mixed integer programming (MIP) methods, in order to solve * exactly * some moderate size, yet difficult, l_{0}-norm sparse approximation problems encountered in various signal processing applications such as spike train deconvolution, hyperspectral unmixing or time series analysis.
First results have shown that:

- exact optimization (that is, computation of the optimal solution with optimality proof) through MIP formulations is possible for some moderate size problems;
- the global minimizer(s) of the l
_{0}problem shows better properties in practice than solutions obtained with state-of-the-art sparse estimation algorithms.

- R. Ben Mhenni, S. Bourguignon, J. Ninin et F. Schmidt, Spectral unmixing with sparsity and structuring constraints, in
*Proc. IEEE WHISPERS*, Amsterdam, The Netherlands, Sep. 2018. - R. Ben Mhenni, S. Bourguignon, J. Ninin et F. Schmidt, Démélange parcimonieux
exact dans une approche supervisée en imagerie hyperspectrale, in
*Actes du 26*, Juan-les-Pins, France, Sep. 2017.[ .pdf ]^{e}colloque GRETSI -
S. Bourguignon, J. Ninin, H. Carfantan and M. Mongeau, Exact sparse
approximation problems via mixed-integer programming: Formulations and
computational performance,
*IEEE Transactions on Signal Processing*, 64(6):1405--1419, March 2016. [ .pdf ]

Ultrasonic inverse problems such as spike train deconvolution, synthetic aperture focusing or tomography aim to reconstruct spatial properties of an object from noisy and incomplete measurements. Such problems rely on both an accurate direct model describing the acquisition process and appropriate prior information constraining the solution. We are interested in modelling acoustic propagation in different kinds of materials, and then in developing appropriate estimation algorithms in order, either to detect discontinuities, delaminations, flaws. etc. (non-destructive testing), or to characterize the inspected material (non-destructive evaluation). First results concerned the deconvolution of spike trains (sparse sequences) in homogeneous, yet attenuative, materials. We are currently working with more complex materials and heterogeneous or anisotropic materials, such as porous and multilayered materials.

- E. Carcreff, S. Bourguignon, J. Idier, and L. Simon, A linear model approach for ultrasonic inverse problems with attenuation and dispersion,
*IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control*, 61(7):1191--1203, July 2014. [ .pdf ] - E. Carcreff, S. Bourguignon, J. Idier, and L. Simon, Resolution enhancement of
ultrasonic signals by up-sampled sparse deconvolution,
*in Proceedings of the IEEE International Conference on Acoustic, Speech and Signal Processing*(Vancouver, Canada, 2013). [ .pdf ]

The development of microwave imaging algorithms has received a lot of interest in the last few years with applications such as biomedical imaging and geoscience. Nonlinear inversion methods are required, which usually rely on iterative algorithms to reconstruct the dielectric properties of the unknown object. Solving the inverse scattering problem under realistic conditions presents several difficulties, a critical one being the computational cost associated with three-dimensional problems. Our work studies new algorithmic strategies in order to reduce the computational cost associated with the optimization problem.

- C. Friedrich, S. Bourguignon, J. Idier, and Y. Goussard, Reconstruction of 3-D microwave images based on a Block-BiCGStab algorithm,
*in**NCMIP, 5th International Workshop on New Computational Methods for Inverse Problems*(Cachan, France, 2015). [ .pdf ] - C. Friedrich, S. Bourguignon, J. Idier, and Y. Goussard, Faster resolution of the 3-D forward problems in microwave imaging by a partial-block BiCGStab algorithm,
*in**EuCAP, The 9th European Conference on Antennas and Propagation*(Lisbon, Portugal, 2015). [ .pdf ]

Fluorescence microscopy is now a classical biological imaging technique. In order to overpass the resolution limit due to the optical system, the structured illumination microscopy (SIM) technique uses modulated illuminations in order to access higher frequencies, that are not directly available through optical observations. By combining numerically several images obtained with different illumination patterns, a super-resolved image can be reconstructed. Recent works have shown that such an image can be obtained, even if the illumination patterns are not known. The so-called blind-SIM approach is then easier to implement, since monitoring illuminations is a difficult task. In this project, we investigate statistical properties of the blind-SIM solution in order to better understand the conditions that guarantee super-resolution. Then, we propose new estimation strategies with more robust statistical properties than the previously proposed method, and we build associated computation algorithms in order to address large 2D (or, in the future, 3D) problems.

- J. Idier
*et al.*, On the super-resolution capacity of imagers using unknown speckle illuminations,*IEEE Transactions on Computational Imaging*, 4(1):87--98, Mar. 2018. [ DOI ] - S. Labouesse
*et al.*, Joint reconstruction strategy for structured illumination microscopy with unknown illuminations,*IEEE Transactions on Image Processing*, 26(5):1--14, mai 2017. [ DOI | http ] - P. Liu
*et al.*, Minimum contrast estimation for super-resolution fluorescence microscopy using speckle patterns, in*Actes du 26*, Juan-les-Pins, Sep. 2017. [ .pdf ]^{e}colloque GRETSI

My main research topic within the ANR DAHLIA project (Dedicated Algorithms for HyperspectraL Imaging in Astronomy) was to develop methods for detection and characterization of astrophysical sources from hyperspectral observations, as those obtained by the MUSE instrument (Multi-Unit Spectroscopic Explorer). This is a difficult issue, mainly because of the size of the data (typically, 300x300 pixels x 4000 wavelengths), the strong level of noise and its spectrally-varying statistics, and high diversity of the searched objects.

- S. Bourguignon, D. Mary, and É. Slezak, Processing muse hyperspectral data:
Denoising, deconvolution and detection of astrophysical sources,
*Statistical Methodology*, 9(1):32--43, 2012. [ .pdf ] - S. Bourguignon, D. Mary, and É. Slezak, Restoration of astrophysical spectra with sparsity constraints: Models and algorithms.,
*IEEE J. Sel. Topics Signal Processing*, 5(5):1002--1013, September 2011.[ .pdf ]

My first research topic concerned the spectral analysis of astronomical time series. The study of many astrophysical phenomena is based on the search for periodicities in light or radial velocity curves. Such time series generally suffer from highly irregular sampling and periodic missing data, due in particular to the alternation of day and night or that of seasons impacting ground-based observations. Thus, Fourier-based spectral analysis may not be satisfactory, and widespread heuristic deconvolution algorithms based on the CLEAN method may lack accuracy. This project addressed spectral analysis as an inverse problem, where the spectrum is discretized on an arbitrarily thin frequency grid. This formulates a deconvolution problem in the Fourier domain. Regularization was addressed by enforcing the sparsity of the solution, as periodic oscillations are searched.
Sparsity was first studied through l_{1}-norm regularization, for which specific algorithms were proposed that allow a very high spectral resolution. A probabilistic modeling of sparsity by a Bernoulli-Gaussian model, combined with Markov Chain Monte-Carlo algorithms, was also studied, which leads to more comprehensive results through a fully unsupervised procedure. In particular, detection probabilities and uncertainties in the estimated parameters are information of prime importance to the astrophysicist, which can be estimated at the price of a much higher computational cost.

- S. Bourguignon, H. Carfantan, and J. Idier, A sparsity-based method for the estimation of spectral lines from irregularly sampled data,
*IEEE Journal of Selected Topics in Signal Processing*, 1(4):575--585, December 2007. [ .pdf ] - S. Bourguignon, H. Carfantan, and T. Boehm, Sparspec: a new method for fitting multiple sinusoids with irregularly sampled,
*Astronomy and Astrophysics*, 462:379--387, January 2007. [ .pdf ] - S. Bourguignon and H. Carfantan, Spectral analysis of irregularly sampled data using a Bernoulli-Gaussian model with free frequencies,
*in**Proceedings of the IEEE International Conference on Acoustic, Speech and Signal Processing*, pp. 516--519 (Toulouse, France, 2006). [ .pdf ]