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- Charles Soussen, JÃ©rÃ´me Idier, David Brie, Junbo Duan
- IEEE Trans. Signal Processing
- 2011

Formulated as a least square problem under an constraint, sparse signal restoration is a discrete optimization problem, known to be NP complete. Classical algorithms include, by increasing cost and efficiency, matching pursuit (MP), orthogonal matching pursuit (OMP), orthogonal least squares (OLS), stepwise regression algorithms and the exhaustive search.â€¦ (More)

- Charles Soussen, RÃ©mi Gribonval, JÃ©rÃ´me Idier, CÃ©dric Herzet
- IEEE Transactions on Information Theory
- 2013

Tropp's analysis of orthogonal matching pursuit (OMP) using the exact recovery condition (ERC) is extended to a first exact recovery analysis of orthogonal least squares (OLS). We show that when the ERC is met, OLS is guaranteed to exactly recover the unknown support in at most <i>k</i> iterations where <i>k</i> denotes the support cardinality. Moreover, weâ€¦ (More)

- CÃ©dric Herzet, Charles Soussen, JÃ©rÃ´me Idier, RÃ©mi Gribonval
- IEEE Transactions on Information Theory
- 2013

We address the exact recovery of a k-sparse vector in the noiseless setting when some partial information on the support is available. This partial information takes the form of either a subset of the true support or an approximate subset including wrong atoms as well. We derive a new sufficient and worst-case necessary (in some sense) condition for theâ€¦ (More)

- Charles Soussen, Ali Mohammad-Djafari
- IEEE Transactions on Image Processing
- 2004

This paper is about three-dimensional (3-D) reconstruction of a binary image from its X-ray tomographic data. We study the special case of a compact uniform polyhedron totally included in a uniform background and directly perform the polyhedral surface estimation. We formulate this problem as a nonlinear inverse problem using the Bayesian framework. Verticeâ€¦ (More)

- Simon Henrot, Charles Soussen, David Brie
- IEEE Transactions on Image Processing
- 2013

In this brief, we provide an efficient scheme for performing deconvolution of large hyperspectral images under a positivity constraint, while accounting for spatial and spectral smoothness of the data.

- CÃ©dric Herzet, AngÃ©lique Dremeau, Charles Soussen
- IEEE Transactions on Information Theory
- 2016

We propose extended coherence-based conditions for exact sparse support recovery using orthogonal matching pursuit and orthogonal least squares. Unlike standard uniform guarantees, we embed some information about the decay of the sparse vector coefficients in our conditions. As a result, the standard condition μ <; 1/(2k - 1) (where μâ€¦ (More)

- Ali Mohammad-Djafari, Charles Soussen
- ICIP
- 2001

We study the 3D reconstruction of a binary scene from X-ray tomographic data. In the special case of a compact and uniform object lying in a uniform background, the scene is entirely defined by the object surface. Then, we select parametric surface models, and we directly estimate their parameters from the data. After showing the ability of sphericalâ€¦ (More)

- SÃ©bastien Bourguignon, Charles Soussen, HervÃ© Carfantan, JÃ©rÃ´me Idier
- 2011 IEEE Statistical Signal Processing Workshopâ€¦
- 2011

Sparse spike train deconvolution is a classical inverse problem which gave rise to many deterministic and stochastic algorithms since the mid-80's. In the past decade, sparse approximation has been an intensive field of research, leading to the development of a number of algorithms including greedy strategies and convex relaxation methods. Spike trainâ€¦ (More)

- Charles Soussen, JÃ©rÃ´me Idier, Junbo Duan, David Brie
- ArXiv
- 2014

Bladder cancer is widely spread in the world. Many adequate diagnosis techniques exist. Video-endoscopy remains the standard clinical procedure for visual exploration of the bladder internal surface. However, videoendoscopy presents the limit that the imaged area for each image is about nearly 1 cm. And, lesions are, typically, spread over several images.â€¦ (More)