Maximum a Posteriori Consistent Estimation Using Interval Analysis

Manel Abid (1) , Michel Kieffer (2, 3) , Beatrice Pesquet-Popescu (1)

1 LTCI - Laboratoire Traitement et Communication de l'Information
2 L2S - Laboratoire des signaux et systèmes
3 IUF - Institut universitaire de France

This paper presents a MAP estimator for some vector $\mathbf{x}$ from its quantized and noisy linear measurements. The complexity of the optimal MAP estimator is intractable in general, and two suboptimal solutions have been proposed, one of which being iterative to be able to handle large-scale problems. Leveraging on techniques from interval analysis, it is possible to quickly eliminate solutions which are not consistent with the signal model, and the quantization noise. These techniques have been applied to the estimation of the input signal of an OFB using noisy measurements of its quantized subbands. The experimental results show that when the channel is noisy, this approach performs better in terms of reconstruction SNR than classical least-squares reconstruction.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Manel Abid, Michel Kieffer, Beatrice Pesquet-Popescu. Maximum a Posteriori Consistent Estimation Using Interval Analysis. SYSID 2012, Jul 2012, Bruxelles, Belgium. pp.1-6. ⟨hal-00727521⟩