Skip to Main content Skip to Navigation
Journal articles

Regularized estimation of mixed spectra using a circular Gibbs-Markov model

Abstract : 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
Complete list of metadatas

https://hal-cea.archives-ouvertes.fr/cea-00333745
Contributor : Philippe Ciuciu <>
Submitted on : Friday, October 24, 2008 - 8:17:13 AM
Last modification on : Wednesday, September 16, 2020 - 4:42:24 PM
Long-term archiving on: : Monday, June 7, 2010 - 9:39:15 PM

Files

SP30762final.pdf
Files produced by the author(s)

Identifiers

Citation

Philippe Ciuciu, J. Idier, Jean-François Giovannelli. Regularized estimation of mixed spectra using a circular Gibbs-Markov model. IEEE transactions on acoustics, speech, and signal processing, Institute of Electrical and Electronics Engineers (IEEE), 2001, 49 (10), pp.2202-13. ⟨10.1109/78.950776⟩. ⟨cea-00333745⟩

Share

Metrics

Record views

578

Files downloads

426