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"Solving Optical Inverse Problems by Promoting Sparsity”

This PhD position opening is now closed

Description:

Nowadays, assuming that a signal (e.g., a 1-D signal, an image or a volume of data) has a sparse representation, i.e., that this signal is linearly described with few elements taken in a suitable basis, is an ubiquitous hypothesis validated in many different scientific domains. Interestingly, this sparsity assumption is the heart of methods solving inverse problems, i.e., estimating a signal from some linear distorting observations. Sparsity stabilizes (or regularizes) these signal estimation techniques often based on L1-norm (or Total Variation norm) minimization and greedy methods.

The PhD project concerns the application of the sparsity principle to solve particular inverse problems occurring in optics. Often with optical sensors, the observation of objects of interest is mainly corrupted by two elements: the noise, either due to the sensor (e.g., electronic/thermic noise) or to the light physics (e.g., Poisson noise), and the Point Spread Function (PSF) of the sensor which blurs (or convolves) the pure image.

The student will develop mathematical methods and algorithms for image denoising and image deconvolution common for confocal microscopy, deflectometry or interferometry, where the sparsity assumption provides significant gains compared to former methods like back-projections, least square methods, or Tikhonov regularization. Connections will be also established with the recent field of compressed sensing, where the sparsity principle really drives the design of innovative optical sensors.

Advisors:
* Prof. Philippe Antoine (IMCN, UCL)
* Dr Laurent Jacques (ICTEAM, UCL)
* Prof. C. De Vleeschouwer (ICTEAM, UCL)
Collaborators:
* Prof. François Chaumont (ISV, UCL)
* Prof. Batoko Henri (ISV, UCL)
* Abdelmounaim Errachid (ISV, UCL)
Industrial Partnership:

Profile:

  • 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,
    • Classical Optics,
    • 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 and advanced high-tech environment, working on leading-edge technologies and having many international contacts.
  • Funding for the beginning of the thesis with the possibility to extend it by a couple of years or to apply for a Belgian NSF grant.

Application:

Applications should include a detailed resume, copy of grade sheets for B.Sc. and M.Sc. Names and complete addresses of referees are welcome.

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

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

Questions about the subject or the position should be addressed to the same email addresses.

Related Biography (just a small subset):

  • I. Daubechies, M. Defrise, C. De Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint", Communications on Pure and Applied Mathematics 57 (2004): pp. 1416-57, PDF
  • F.-X. Dupé , M.J. Fadili, J-L. Starck, "Image deconvolution under Poisson noise using sparse representations and proximal thresholding iteration" , ICASSP 2008, Las Vegas, USA, 2008. PDF
  • Richard Baraniuk, "Compressive sensing", IEEE Signal Processing Magazine, 24(4), pp. 118-121, July 2007). PDF
  • L. Jacques and P. Vandergheynst, "Compressed Sensing: When sparsity meets sampling", In "Optical and Digital Image Processing - Fundamentals and Applications", Edited by G. Cristòbal; P. Schelkens; H. Thienpont. In press in 2010. PDF