Σ-Vision (Sparsity, Image and Geometry to Model Adaptively Visual Processings) is a research group financed by the ERC Starting Grant program. Σ-Vision will develop the next generation algorithms and methodologies for image processing. These algorithms will rely on several mathematical breakthroughs in image modeling: structured sparsity, geometric representations and adaptivity. They will be implemented using fast optimization codes that can handle massive datasets with gigapixels images and videos. These algorithms will have far reaching applications in computer vision, graphics and neuroscience. These cutting edge mathematical approaches will go beyond traditional image processing scenarios and impact significantly object recognition, dynamical special effects and exploration of the visual cortex.

 

 

Research Interests

Theme 1 - Theoritical guarantees for sparse regularization: We analyze theoritically the performances of various kind of sparse regularizations in the framework of imaging problems (super-resolution, tomography, compressed sensing, etc.). The goal is to design data-dependent criteria that take into account the geometry of the signal and its interaction with the imaging operator.

Theme 2 - Mathematical modeling of dynamical textures: We develop deterministic and stochastic models of natural textures that take into account both the texture material (albedo, illumination, reflectance, etc) and its time dynamic. We propose novel statistical estimators based on the theory of optimal transport that allows us to interactively navigate in a database of textures for computer graphics applications.

Theme 3 - Modeling the visual brain dynamics: We propose an integrated pipeline for the modeling and the processing of cortical imaging data. In particular, we develop tools to model the brain dynamics observed using Voltage Sensitive Dye Optical Imaging and multi-electrodes arrays recordings.

Team Members

Permanent members:

PhD and post-docs:

Former students:

Collaborators:

Publications

2014
[28] Optimal Transport with Proximal Splitting (N. Papadakis, G. Peyré, E. Oudet), SIAM Journal on Imaging Sciences, vol. 7(1), pp. 212–-238, 2014. (code) [bib] [pdf] [doi]
2013
[27] Synthesizing and Mixing Stationary Gaussian Texture Models (G-S. Xia, S. Ferradans, G. Peyré, J-F. Aujol), to appear in SIAM Journal on Imaging Sciences, 2013. [bib] [pdf]
[26] Model Selection with Piecewise Regular Gauges (S. Vaiter, M. Golbabaee, J. Fadili, G. Peyré), Technical report, Preprint hal-00842603, 2013. [bib] [pdf]
[25] Constrained Sparse Texture Synthesis (G. Tartavel, Y. Gousseau, G. Peyré), Proc. SSVM'13, 2013. [bib] [pdf]
[24] Regularized Discrete Optimal Transport (S. Ferradans, N. Papadakis, G. Peyré, J-F. Aujol), Proc. SSVM'13, 2013. [bib] [pdf]
[23] Optimal Transport Mixing of Gaussian Texture Models (S. Ferradans, G-S. Xia, G. Peyré, J-F. Aujol), Proc. SSVM'13, 2013. [bib] [pdf]
[22] Stein COnsistent Risk Estimator (SCORE) for hard thresholding (C. Deledalle, G. Peyré, J. Fadili), Proc. SPARS'13, 2013. [bib] [pdf]
[21] Robust Polyhedral Regularization (S. Vaiter, G. Peyré, J. Fadili), Proc. Sampta'13, 2013. [bib] [pdf]
[20] Stable Recovery with Analysis Decomposable Priors (J. Fadili, G. Peyré, S. Vaiter, C. Deledalle, J. Salmon), Proc. Sampta'13, 2013. [bib] [pdf]
[19] A Generalized Forward-Backward Splitting (H. Raguet, J. Fadili, G. Peyré), SIAM Journal on Imaging Sciences, vol. 6(3), pp. 1199-1226, 2013. (code) [bib] [pdf] [doi]
[18] The degrees of freedom of penalized l1 minimization (C. Dossal, M. Kachour, J. Fadili, G. Peyré, C. Chesneau), Statistica Sinica, vol. 23(2), pp. 809-828, 2013. [bib] [pdf] [doi]
[17] Regularized Discrete Optimal Transport (S. Ferradans, N. Papadakis, G. Peyré, J-F. Aujol), Technical report, Preprint arxiv-1307.5551, 2013. [bib] [pdf]
[16] Exact Support Recovery for Sparse Spikes Deconvolution (V. Duval, G. Peyré), Technical report, Preprint hal-00839635, 2013. [bib] [pdf]
[15] Finsler Steepest Descent with Applications to Piecewise-regular Curve Evolution (G. Charpiat, G. Nardi, G. Peyré, F-X. Vialard), Technical report, Preprint hal-00849885, 2013. [bib] [pdf]
[14] Variational Texture Synthesis with Sparsity and Spectrum Constraints (G. Tartavel, Y. Gousseau, G. Peyré), Technical report, Preprint Hal-00881847, 2013. [bib] [pdf]
[13] Iteration-Complexity of a Generalized Forward Backward Splitting Algorithm (J. Liang, J. Fadili, G. Peyré), Technical report, Preprint arXiv:1310.6636, 2013. [bib] [pdf]
[12] Sliced and Radon Wasserstein Barycenters of Measures (N. Bonneel, J. Rabin, G. Peyré, H. Pfister), Technical report, Preprint Hal-00881872, 2013. [bib] [pdf]
[11] Robust Sparse Analysis Regularization (S. Vaiter, G. Peyré, C. Dossal, J. Fadili), IEEE Transactions on Information Theory, vol. 59(4), pp. 2001-2016, 2013. [bib] [pdf] [doi]
2012
[10] The degrees of freedom of the Group Lasso for a General Design (S. Vaiter, C. Deledalle, G. Peyré, J. Fadili, C. Dossal), Technical report, Preprint Hal-00768896, 2012. [bib] [pdf]
[9] Local Behavior of Sparse Analysis Regularization: Applications to Risk Estimation (S. Vaiter, C. Deledalle, G. Peyré, J. Fadili, C. Dossal), to appear in Applied and Computational Harmonic Analysis, 2012. [bib] [pdf] [doi]
[8] Proximal Splitting Derivatives for Risk Estimation (C. Deledalle, S. Vaiter, G. Peyré, J. Fadili, C. Dossal), Proc. NCMIP'12, 2012. [bib] [pdf]
[7] Nonlocal Active Contours (M. Jung, G. Peyré, L. D. Cohen), SIAM Journal on Imaging Sciences, vol. 5(3), pp. 1022-1054, 2012. [bib] [pdf] [doi]
[6] Risk estimation for matrix recovery with spectral regularization (C. Deledalle, S. Vaiter, G. Peyré, J. Fadili, C. Dossal), Proc. ICML'12 Workshops, 2012. [bib] [pdf]
[5] Degrees of Freedom of the Group Lasso (S. Vaiter, C. Deledalle, G. Peyré, J. Fadili, C. Dossal), Proc. ICML'12 Workshops, 2012. [bib] [pdf]
[4] Wasserstein Active Contours (G. Peyré, J. Fadili, J. Rabin), Proc. ICIP'12, 2012. [bib] [pdf]
[3] Unbiased Risk Estimation for Sparse Analysis Regularization (C. Deledalle, S. Vaiter, G. Peyré, J. Fadili, C. Dossal), Proc. ICIP'12, 2012. [bib] [pdf]
[2] Compact Representations of Stationary Dynamic Textures (G-S. Xia, S. Ferradans, G. Peyré, J-F. Aujol), Proc. ICIP'12, 2012. [bib] [pdf]
[1] Sharp Support Recovery from Noisy Random Measurements by L1 minimization (C. Dossal, M.L. Chabanol, G. Peyré, J. Fadili), Applied and Computational Harmonic Analysis, vol. 33(1), pp. 24-43, 2012. [bib] [pdf] [doi] [cites]
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