Research topics
of Laurent Condat
Mathematical and computational signal and image processing: inverse problems, variational methods, convex optimization, sampling, color and multispectral imaging.
Largescale 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 forwardbackward view of some primaldual 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. 10541057, Aug. 2014. PDF. Matlab
files: optimization.zip

L. Condat,
“A primaldual splitting method for convex optimization involving
Lipschitzian, proximable and linear composite terms,” J.
Optimization Theory and Applications, vol. 158, no. 2, pp. 460479,
2013. PDF
L. Condat,
“Fast projection onto the simplex and the l1 ball,” Mathematical Programming Series A, vol. 158, no. 1, pp. 575585, July 2016. PDF. Supplementary 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. 10541057, 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
Superresolution
Superresolution 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. 1747, 2015.
PDF. Matlab file: pulses_recovery.m

L. Condat and A. Hirabayashi, “Superresolution of positive spikes by Toeplitz lowrank approximation,” EUSIPCO, Sept. 2015,
Nice, France. PDF

L. Condat, J.
Boulanger, N. Pustelnik, S. Sahnoun, and L. Sengmanivong, “A 2D
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. BioucasDias, 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. 41604174, 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. 10541057, 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. PDF. Matlab
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. 22002210, Aug. 2011. PDF. Matlab
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. 11961202, Aug. 2010. PDF. Matlab
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 cyanmagentayellow counterpart is very good as well):
(CFA_Condat_18.tif)
Sampling and reconstruction in linear shiftinvariant
spaces
Slides summarizing my contributions on the subject: PDF
