The Institut de Mathématiques de Marseille (UMR 7373) proposes a (4 to 6 months) master internship for the spring 2018 (start date: march 2018), on Source separation algorithms for NMR spectroscopy. The training period will take place in the Signal and Image team of the Institut de Mathématiques de Marseille, 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 advisors are:
The training period should last at least 4 months between March 2018 and September 2018. The trainee will receive around 550 euros per month (net salary).
Candidates should send a résumé to email@example.com and firstname.lastname@example.org showing their motivation and capabilities in developing an advanced research project in applied mathematics (optimization), signal/image processing (inverse problems) and computer science (programming in Matlab and/or python). They should be at graduate level (second year of Master or equivalent).
Nuclear Magnetic Resonance (NMR) spectroscopy  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 training period is about blind source separation. 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 of observations X (NMR spectra of mixtures), one wants to estimate matrices A (mixing matrice) and S (sources, pure spectra) such that X ≈ AS
The aim of this internship is to develop stable blind source separation  algorithms producing high-purity source representation in the presence of signal distortions and instabilities. The methods will be applied to NMR spectroscopy data of complex mixtures, with a focus on multidimensional data. Previous results have shown that approaches based on non-negative matrix factorizations and/or sparsity of the sources lead to rather satisfactory results, in the case of one-dimensional spectra. Multidimensional spectra will be also studied for which sparsity is expected to play an even greater role.
During the internship, after a first phase of introduction to the subject (discussions with supervisors and bibliographic work), the main activities of the trainee will be to implement under Matlab or Python standard and state of the art separation algorithms (either adapted to one-dimensional or specific approaches for the multidimensional case), develop and study extensions adapted to NMR spectroscopy applications, and to test, compare and validate them on simulated and real datasets.
The internship therefore includes not only bibliographic and theoretical components, but also a programming and application to real data components.
 Timothy D.W. Claridge, High-Resolution NMR Techniques in Organic Chemistry, Third Edition, Elsevier Science, 2016.
 Source Separation and Applications, IEEE Signal Processing Magazine, Vol. 31, No. 3, May 2014.
(c) GdR 720 ISIS - CNRS - 2011-2018.