CLOSED

# Opening of a PhD position:

 Low-Dimensional Prior Models for Hyperspectral Images and Applications

closed

## Project Summary:

The objective of this project is to sustain the realization of a PhD thesis under the supervision of Prof. Laurent Jacques (ICTEAM, UCL) and with the help of Prof. Christophe De Vleeschouwer (ICTEAM, UCL) in the general topic of Low-Dimensional Prior Models for Hyperspectral Images and Applications.

More precisely, the project aims at efficiently representing the high-dimensional signal acquired with Hyperspectral imaging where a given object is observed in a dense set of wavelengths.

The theoretical tools that will sustain these new models pertain to the general fields of computational harmonic analysis (or sparse analysis) [Mal99], low-rank data representations [Faz08], or hybrid models [Gol12]. Disposing of such an efficient hyperspectral data representation, i.e., a model which minimizes the number of parameters needed to represents spatio-spectral features, is of paramount importance for facing three different challenges targeted by this project:

• Compression of hyperspectral data: the high-dimensionality of the hyperspectral data often involves subsequent compression methods. Currently, these hardly consider the geometry of the spatio-spectral domain. Most often each spectral band is compressed separately (e.g., using wavelet compression schemes) discarding the information contained in spectral correlations.
• Non-linear hyperspectral data restoration: hyperspectral images suffer from several data corruptions that must be removed or reduced, such as noises (Poisson, Gaussian, or readout noises), missing informations (corrupted pixels, dead areas), instrumental response (or point-spread-function), subsampling (sensor with limited resolution) or data quantization/digitalization process (e.g., for storage or transmission needs).
• Compressive hyperspectral imaging: the question of compressing hyperspectral data directly at the acquisition stage, as advocated by the compressed sensing theory [Can06], is of prime interest in order to improve common sensing procedures, e.g., to make them faster, more power efficient and/or with reduced communication levels. The decoding stage reconstructing compressively acquired data must also be as light as possible with the development of efficient algorithms [Com11].

The expected project achievements will have interesting impacts, for instance, in medical or in satellite imaging, where accurate characterization of skin diseases (e.g., melanoma) or of terrestrial areas (e.g., forests or soils) must be realized from their specific spectral signatures, or in automatic food quality control where spectral signature modifications are related to undesired food alterations.

• [Can06] E. Candès, J. Romberg and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Comm. Pure and Appl. Math., 59(8):1207–1223, 2006. (pdf)
• [Mal99] S. Mallat, “A Wavelet Tour of Signal Processing”. Academic Press, 1999.
• [Gol12] M. Golbabaee, P. Vandergheynst. "Hyperspectral image compressed sensing via low-rank and joint-sparse matrix recovery." IEEE ICASSP Int. Conf., 2012. (pdf)
• [Com11] P. L. Combettes, J.-C. Pesquet. "Proximal splitting methods in signal processing." Fixed-Point Algorithms for Inverse Problems in Science and Engineering (2011): 185-212. (pdf)
• [Faz08] M. Fazel, E. Candes, B. Recht, P. Parrilo, “Compressed sensing and robust recovery of low rank matrices”. In Sig., Syst. Comp., 42nd IEEE Asilomar Conf., pp. 1043-1047, 2008.

## Job description:

The student will develop mathematical models and algorithms for the objectives described above. Research activity will be carried out in the Image and Signal Processing Group (ISP Group) in ICTEAM/ELEN, UCL, in collaborations with international teams (in Europe and USA) and industrial partners.

## Candidate's Profile:

The position is reserved for candidate with very high profile (high grades). He/she must be graduated since no more than one year (funding requirement).

More particularly, we expect from him/her:

• a M.Sc. in Applied Mathematics, Physics, Electrical Engineering, or Computer Science;
• Knowledge (even partial) in the following topics constitutes assets:
• Convex Optimization methods,
• Signal/Image Processing,
• Compressed Sensing and inverse problems.
• Experience with Matlab, C and/or C++.
• Good communications skills, both written and oral;
• Speaking fluently in English (or French) is required. Writing in English is mandatory.

## We offer:

• A research position in a dynamic environment, working on leading-edge theories/methods/technologies with many international contacts.
• The funding is granted for 12 to 15 months starting on October 1st, 2013.
• During this first grant, the selected candidate will have to apply to a Belgian NSF grant (FNRS or FRIA) for completing his PhD program (4 years).
• Salary is around 1600-1700 euros/month (netto, after taxes and social security coverage).
• The candidate will have also to subscribe the standard PhD program of UCL.

## Application:

Applications should include

• a detailed resume,
• copy of grade sheets for B.Sc. and M.Sc.
• (if available, a pdf copy of one personal publication of interest or master project summary)
• Names and complete addresses of referees are welcome.

Please send applications by email to (replace _AT_ and _DOT_):

	laurent.jacques _AT_ uclouvain _DOT_ be
christophe.devleeschouwer _AT_ _uclouvain _DOT_ be