29 mai 2018

Catégorie : Post-doctorant

A two years PostDoc position is available at Institut de Mathématiques de Marseille (a joint research unit of Aix-Marseille University, CNRS and Centrale Marseille), France, to start in the fall 2018, in the framework of the BIFROST (Blind Identification, Filtering & Restoration On Spectral Techniques) project. The main topic of the PostDoc project is source separation for NMR spectroscopy signals, which involves various domains such as signal processing, applied mathematics, optimization and statistics, as well as validation on simulated and real datasets (provided by BIFROST partners).

We are seeking to recruit a junior post doctorial associate with a demonstrated potential to develop an independent research career. Candidates are expected to hold a PhD in applied mathematics, with experience (or at least strong interest) in signal processing, or in signal or image processing with strong mathematical background. The recruited scientist will work in the Signal-Image team at I2M, and collaborate with the BIFROST partners (ISM2, Institut des Sciences Moléculaires de Marseille, and IFPen (IFP Energies Nouvelles)).

Applications, to be sent by email as soon as possible and before **June 25, 2018** to Dr Caroline Chaux (caroline.chaux@univ-amu.fr), should include the candidate’s CV, with publication list, a motivation letter and (at least two) reference letters.

The expected start date is October 1st 2018, the date can be modified depending on the candidate’s availability.

Nuclear Magnetic Resonance (NMR) spectroscopy [1] is a magnetic spectroscopy involving samples that are often bio organic molecules such as small metabolites or protein. NMR spectrocopy records signals (spectra) coming from atomic kernels and more precisely from isotopes. Such spectra are acquired directly in the Fourier domain. When observing complex mixtures, the observed spectra constitute a mix of several pure spectra. The aim is to recover which compounds are present in a mixture and in which proportion.

From the mathematical and signal processing point of view, this PostDoc project is about blind source separation (see [2] for a recent review). The problem is to estimate jointly unknown sources which are linearly combined with unknown mixing coefficients, from observed signals. In other words, given a matrix (or a tensor in the nD situation) of observations X (NMR spectra of mixtures), one wants to estimate a mixing matrix A and a source matrix (or tensor) S containing pure spectra such that the data matrix (or tensor) factorizes as a product of the mixing matrix with source matrix (or tensor).

The project involves several aspects, including

- Blind and semi-blind source separation for 1D NMR spectroscopy data, mainly (non-negative) matrix factorization techniques, extending state of the art and earlier results by the team. In semi-blind approaches, the goal is to include prior informations in the identification algorithms;
- Integration within identification algorithms of several pre-processing steps usually involved in NMR data acquisition;
- Extensions to 2D and nD NMR spectroscopy data;
- Participation in the development of a benchmark signals database, and test and validation of algorithms on corresponding data.

The recruited PostDoc will work in these directions in collaboration with the teams of the BIFROST project. Besides the scientific activity, the recruited PostDoc will participate actively in the organization of the project (manage agenda, organize meetings, participate in reporting), and the supervision of students (at Master and possibly PhD levels).

BIFROST is a three years project funded by the excellence initiative A*MIDEX, at the interface of analytical chemistry and applied mathematics. BIFROST concerns the development of data processing and data acquisition schemes capable of improving the power of chemical analysis of complex mixtures, in view of achieving a qualitative and quantitative decomposition of instrumental responses, loosely called spectra hereafter. This will be achieved by addressing bottlenecks in both disciplines, as detailed below. The challenge resides in producing stable algorithms producing highpurity source representation in the presence of signal distortions and instabilities and, more importantly, a wide dynamic range of molecular concentrations. This last aspect is crucial for several reasons. From the chemical point of view, the most abundant compounds not always carry relevant information about the state of a sample, with biomarkers and contaminants being typical examples of this. The most intricate case of study is the one in which the spectrum presents severe overlap, so that more intense signals are likely to obscure the ones from minor species. Thus, an obvious avenue of investigation to improve the detection of less abundant compounds is to seek analytical techniques with increased resolution. This can be achieved for instance by physical separation of the sample into simpler portions (to the limit case of pure compounds). Multidimensional (nD) analyses are a possible response to this approach that has been extensively researched. Possibly, the richest selection of nD experiments can be found in the field of Nuclear Magnetic Resonance, with tens of methods available. Other spectral techniques, such as chromatography and mass spectrometry (MS) also rely more and more on nD combinations (sometimes called hyphenation). Intriguingly, signal processing, namely covariance analysis, has been used with some success to create the equivalent of nD spectra by relying on variations of the signal intensity along series of samples.

From the mathematical viewpoint, the unmixing problem is a blind source separation problem, which can also be seen as an instance of the dictionary learning problem, which currently receives considerable attention. Dictionary learning generally leads to difficult non-convex optimization problems, for which there exist very few provably convergent and stable algorithms. Developing such algorithms for spectroscopy unmixing is by itself a very challenging goal. The NMF (Nonnegative Matrix Factorization) based approach developed earlier by the consortium has been shown to yield good separation results in some specific situations, but has not been developed so far for nD experiments, and lacks theoretical convergence guarantees. Alternative strategies must be investigated.

A main goal of this project is to develop mathematical and signal processing approaches that stay as close as possible to signal acquisition, e.g. avoiding “black box” pre-processing methods and software. The problem is to integrate such pre-processings in the unmixing problem. Another goal will be to integrate prior knowledge in the unmixing, e.g. knowledge about spectra of some of the compounds (for example biomarkers or contaminants).

The post-doc will take place in the Signal and Image team (https://www.i2m.univ-amu.fr/Equipe-Signal-et-Image-SI) of the Institut de Mathématiques de Marseille (https://www.i2m.univ-amu.fr), which is a joint research center between Aix -Marseille University, Ecole Centrale Marseille and CNRS (Centre National de la Recherche Scientifique). The Signal and Image team at I2M is easily accessible from downtown Marseille by public transportation (Metro Line 1 in the direction of La Rose until the last station La Rose. Then Bus B3B direction Technopôle de Château Gombert until the Technopôle Polytech Marseille stop).

The recruited PostDoc will also work regularly with the BIFROST partners, ISM2 (Institut des Sciences Moléculaires de Marseille, Campus Saint Jérôme - service 531, avenue Escadrille Normandie-Niémen, 13397 Marseille cedex 20) on the St Jérôme campus, easily accessible from downtown as well as I2M by public transportations and IFPEN (located in Rueil-Malmaison near Paris).

The salary is 2300 (net salary).

[1] Timothy D.W. Claridge, High-ResolutionNMRTechniques in Organic Chemistry, Third Edition, Elsevier Science, 2016.

[2] Source Separation and Applications, IEEE Signal Processing Magazine, Vol. 31, No. 3, May 2014.

(c) GdR 720 ISIS - CNRS - 2011-2018.