Service interruption on Monday 11 July from 12:30 to 13:00: all the sites of the CCSD (HAL, EpiSciences, SciencesConf, AureHAL) will be inaccessible (network hardware connection).
Skip to Main content Skip to Navigation

Orthogonal greedy algorithms for non-negative sparse reconstruction

Abstract : Non-negative sparse approximation arises in many applications fields such as biomedical engineering, fluid mechanics, astrophysics, and remote sensing. Some classical sparse algorithms can be straightforwardly adapted to deal with non-negativity constraints. On the contrary, the non-negative extension of orthogonal greedy algorithms is a challenging issue since the unconstrained least squares subproblems are replaced by non-negative least squares subproblems which do not have closed-form solutions. In the literature, non-negative orthogonal greedy (NNOG) algorithms are often considered to be slow. Moreover, some recent works exploit approximate schemes to derive efficient recursive implementations. In this thesis, NNOG algorithms are introduced as heuristic solvers dedicated to L0 minimization under non-negativity constraints. It is first shown that the latter L0 minimization problem is NP-hard. The second contribution is to propose a unified framework on NNOG algorithms together with an exact and fast implementation, where the non-negative least-square subproblems are solved using the active-set algorithm with warm start initialization. The proposed implementation significantly reduces the cost of NNOG algorithms and appears to be more advantageous than existing approximate schemes. The third contribution consists of a unified K-step exact support recovery analysis of NNOG algorithms when the mutual coherence of the dictionary is lower than 1/(2K-1). This is the first analysis of this kind.
Complete list of metadata

Cited literature [117 references]  Display  Hide  Download
Contributor : Thi-Thanh Nguyen Connect in order to contact the contributor
Submitted on : Friday, November 22, 2019 - 6:26:35 PM
Last modification on : Wednesday, November 3, 2021 - 7:56:32 AM


Files produced by the author(s)


  • HAL Id : tel-02376895, version 1


Thi Thanh Nguyen. Orthogonal greedy algorithms for non-negative sparse reconstruction. Engineering Sciences [physics]. Université de Lorraine, 2019. English. ⟨NNT : 2019LORR0133⟩. ⟨tel-02376895⟩



Record views


Files downloads