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  Research topics of Laurent Condat

   Mathematical and computational signal and image
   processing: inverse problems, variational methods,
   convex optimization, sampling, color and multispectral
   imaging.













Large-scale convex nonsmooth optimization

Finding an optimal element with respect to a sum of antagonist cost functions allows to solve regularized inverse imaging problems. Optimization is of primary importance in many other fields, like genomics, finance...  The difficulty stems from the very large number of variables to optimize, e.g. the number of pixels if the unknown element is an image.

Main papers:
  • P. L. Combettes, L. Condat, J.-C. Pesquet, and B. C. Vũ, “A forward-backward view of some primal-dual optimization methods in image recovery,” IEEE ICIP, Oct. 2014, Paris, France. PDF

  • L. Condat, “A Generic Proximal Algorithm for Convex Optimization - Application to Total Variation Minimization,” IEEE Signal Proc. Letters, vol. 21, no. 8, pp. 1054-1057, Aug. 2014.  PDF Matlab files:  optimization.zip

  • L. Condat, “A primal-dual splitting method for convex optimization involving Lipschitzian, proximable and linear composite terms,” J. Optimization Theory and Applications, vol. 158, no. 2, pp. 460-479, 2013.  PDF

  • L. Condat, “Fast projection onto the simplex and the l1 ball,” Mathematical Programming Series A, vol. 158, no. 1, pp. 575-585, July 2016.  PDFSupplementary material: C code  condat_simplexproj.c  condat_l1ballproj.c .  Matlab code: proj_simplex_l1ball.m

  • L. Condat, “A direct algorithm for 1D total variation denoising,” IEEE Signal Proc. Letters, vol. 20, no. 11, pp. 1054-1057, Nov. 2013.  PDF C file:  condat_fast_tv.c.  For use in Matlab, mex files made by Stephen Becker.
    New, 2017: A new, even better, algorithm: Matlab code and C code


Super-resolution

Super-resolution consists in recovering a signal with a better precision than what seems possible given the resolution limit of the available measurements, by making use of prior knowledge on the signal structure.

Main papers:
  • L. Condat and A. Hirabayashi, “Cadzow denoising upgraded: A new projection method for the recovery of Dirac pulses from noisy linear measurements,” Sampling Theory in Signal and Image Processing, vol. 14, no. 1, pp. 17-47, 2015.  PDF.  Matlab file: pulses_recovery.m

  • L. Condat and A. Hirabayashi, “Super-resolution of positive spikes by Toeplitz low-rank approximation,” EUSIPCO, Sept. 2015, Nice, France.  PDF

  • L. Condat, J. Boulanger, N. Pustelnik, S. Sahnoun, and L. Sengmanivong, “A 2-D spectral analysis method to estimate the modulation parameters in structured illumination microscopy,” IEEE ISBI, Apr. 2014, Beijing, China.  PDF.


Multispectral image processing

Hyperspectral imaging devices produce a stack of images, where each image represents information in a narrow band of the electromagnetic spectrum. Processing such data requires modelling the spatial and spectral interactions of the physical elements composing the scene.

Main papers:
  • A. Tiard, L. Condat, L. Drumetz, J. Chanussot, W. Yin, and X. Zhu, “Robust linear unmixing with enhanced sparsity,” IEEE ICIP, Sept. 2017, Beijing, China.  PDF

  • X. He, L. Condat, J. Bioucas-Dias, J. Chanussot and J. Xia, “A new pansharpening method based on spatial and spectral sparsity priors,” IEEE Transactions on Image Processing, vol. 23, no. 9, pp. 4160-4174, Sept. 2014. PDF.


Color image processing for digital photography

In digital cameras, the sensor is overlaid with an array of color filters. The choice of these filters and of the reconstruction method from the partial and noisy information acquired, in order to obtain clean and accurate full color images, are difficult but crucial problems.

Main papers:
  • L. Condat, “A Generic Proximal Algorithm for Convex Optimization - Application to Total Variation Minimization,” IEEE Signal Proc. Letters, vol. 21, no. 8, pp. 1054-1057, Aug. 2014.  PDF Matlab files:  optimization.zip

  • L. Condat and S. Mosaddegh, “Joint Demosaicking and Denoising by Total Variation Minimization,” IEEE ICIP, Sept. 2012, Orlando, USA.  PDFMatlab files:  denoisaicking_TV_Condat.zip

  • L. Condat, “A new color filter array with optimal properties for noiseless and noisy color image acquisition,” IEEE Transactions on Image Processing, vol. 20, no. 8, pp. 2200-2210, Aug. 2011.  PDFMatlab files:  denoisaicking_Condat.zip

  • L. Condat, “Color filter array design using random patterns with blue noise chromatic spectra,” Image and Vision Computing, vol. 28, no. 8, pp. 1196-1202, Aug. 2010.  PDFMatlab files:  CFArandom1.m   CFArandom2.m

Slides summarizing my contributions on the subject: PDF

Note: if you want to use a random color filter array (CFA) with blue noise properties without the hassle of generating it, consider as a very good approximation this 18x18 pattern with periodization (its cyan-magenta-yellow counterpart is very good as well):
(CFA_Condat_18.tif)

Sampling and reconstruction in linear shift-invariant spaces

Slides summarizing my contributions on the subject: PDF