cea-00333745
https://cea.hal.science/cea-00333745
https://cea.hal.science/cea-00333745/document
https://cea.hal.science/cea-00333745/file/SP30762final.pdf
doi:10.1109/78.950776
[CEA] CEA - Commissariat à l'énergie atomique
[UNIV-NANTES] Université de Nantes
[EC-PARIS] Ecole Centrale Paris
[CNRS] CNRS - Centre national de la recherche scientifique
[UNIV-PSUD] Université Paris Sud - Paris XI
[EC-NANTES] Ecole Centrale de Nantes
[IRCCYN] Institut de Recherche en Communication et Cybernétique de Nantes
[IRCCYN-ADTSI] Analyse et Décision en Traitement du Signal et Images
[SUP_LSS] Laboratoire des Signaux et Systèmes
[UNAM] l'unam - université nantes angers le mans
[UNIV-PARIS-SACLAY] Université Paris-Saclay
[UNIV-PSUD-SACLAY] Université Paris Sud pour Paris Saclay
[NANTES-UNIVERSITE] Nantes Université
[UNIV-NANTES-AV2022] Université de Nantes
[NU-CENTRALE] École Centrale de Nantes
[TEST3-HALCNRS] TEST3-HALCNRS
Regularized estimation of mixed spectra using a circular Gibbs-Markov model
Ciuciu, Philippe
Idier, J.
Giovannelli, Jean-François
[SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing
[INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing
ART
spectral estimation
mixed spectra
convex analysis
Gibbs-Markov
line spectra
reguylarization
Formulated as a linear inverse problem, spectral estimation is particularly underdetermined when only short data sets are available. Regularization by penalization is an appealing nonparametric approach to solve such ill-posed problems. Following Sacchi et al. (see ibid., vol.46, no.1, p.32-38, 1998), we first address line spectra recovering in this framework. Then, we extend the methodology to situations of increasing difficulty: the case of smooth spectra and the case of mixed spectra, i.e., peaks embedded in smooth spectral contributions. The practical stake of the latter case is very high since it encompasses many problems of target detection and localization from remote sensing. The stress is put on adequate choices of penalty functions: following Sacchi et al., separable functions are retained to retrieve peaks, whereas Gibbs-Markov potential functions are introduced to encode spectral smoothness. Finally, mixed spectra are obtained from the conjunction of contributions, each one bringing its own penalty function. Spectral estimates are defined as minimizers of strictly convex criteria. In the cases of smooth and mixed spectra, we obtain nondifferentable criteria. We adopt a graduated nondifferentiability approach to compute an estimate. The performance of the proposed techniques is tested on the well-known Kay and Marple (1982) example
2001-10-01
2008-10-24
en
IEEE transactions on acoustics, speech, and signal processing
Institute of Electrical and Electronics Engineers (IEEE)