Charles Soussen

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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.(More)
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, we(More)
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 the(More)
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. Vertice(More)
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 &#x03BC; &lt;; 1/(2k - 1) (where &#x03BC;(More)
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 train(More)
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.(More)