arXiv subjects

Sébastien Bourguignon

Publications and source records attributed to Sébastien Bourguignon.

4 recordsLinked to original sources

arXiv2025

An active-set algorithm for spectral unmixing

Linear spectral unmixing under nonnegativity and sum-to-one constraints is a convex optimization problem for which many algorithms were proposed. In practice, especially for supervised unmixing (i.e., with a large dictionary), solutions tend to be sparse due to the nonnegativity of the abundances, thereby motivating the use of an active-set solver. Given the problem specific features, it seems advantageous to design a dedicated algorithm in order to gain computational performance compared to generic solvers. In this paper, we propose to derive such a specific algorithm, while extending the nonnegativity constraints to broader minimum abundance constraints.

eess.SP↗

arXiv2021

SLS (Single $\ell_1$ Selection): a new greedy algorithm with an $\ell_1$-norm selection rule

In this paper, we propose a new greedy algorithm for sparse approximation, called SLS for Single L_1 Selection. SLS essentially consists of a greedy forward strategy, where the selection rule of a new component at each iteration is based on solving a least-squares optimization problem, penalized by the L_1 norm of the remaining variables. Then, the component with maximum amplitude is selected. Simulation results on difficult sparse deconvolution problems involving a highly correlated dictionary reveal the efficiency of the method, which outperforms popular greedy algorithms and Basis Pursuit Denoising when the solution is sparse.

math.OC↗

arXiv2017

On the super-resolution capacity of imagers using unknown speckle illuminations

Speckle based imaging consists of forming a super-resolved reconstruction of an unknown sample from low-resolution images obtained under random inhomogeneous illuminations (speckles). In a blind context where the illuminations are unknown, we study the intrinsic capacity of speckle-based imagers to recover spatial frequencies outside the frequency support of the data, with minimal assumptions about the sample. We demonstrate that, under physically realistic conditions, the covariance of the data has a super-resolution power corresponding to the squared magnitude of the imager point spread function. This theoretical result is important for many practical imaging systems such as acoustic and electromagnetic tomographs, fluorescence and photoacoustic microscopes, or synthetic aperture radar imaging. A numerical validation is presented in the case of fluorescence microscopy.

physics.data-an↗

arXiv2017

Joint reconstruction strategy for structured illumination microscopy with unknown illuminations

The blind structured illumination microscopy (SIM) strategy proposed in (Mudry et al., 1992) is fully re-founded in this paper, unveiling the central role of the sparsity of the illumination patterns in the mechanism that drives super-resolution in the method. A numerical analysis shows that the resolving power of the method can be further enhanced with optimized one-photon or two-photon speckle illuminations. A much improved numerical implementation is provided for the reconstruction problem under the image positivity constraint. This algorithm rests on a new preconditioned proximal iteration faster than existing solutions, paving the way to 3D and real-time 2D reconstruction

physics.data-an↗