Towards interval-based non-additive deconvolution in signal processing

Olivier Strauss (1) , Agnès Rico (2)

1 ICAR - Image & Interaction
2 ERIC - Equipe de Recherche en Ingénierie des Connaissances

Reconstructing a signal from its observations via a sensor device is usually called "deconvolution". Such reconstruction requires perfect knowledge of the impulse response of the sensor involved in the signal measurement. The lower this knowledge, the more biased the reconstruction. In this paper, we present a novel method for reconstructing a signal measured by a sensor whose impulse response is imprecisely known. This technique is based on modeling the relationship between the measurement and the signal via a concave capacity and extending the convolution concept to a concave set of impulse responses. The reconstructed signal is interval-valued, thus reflecting the poor knowledge of the sensor impulse response.

Mots clés: Inverse problem; Deconvolution; Non-additive confidence measure; Choquet integral; Schultz iterative procedure

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

Olivier Strauss, Agnès Rico. Towards interval-based non-additive deconvolution in signal processing. Soft Computing, 2012, 16 (5), pp.809-820. ⟨10.1007/s00500-011-0771-7⟩. ⟨lirmm-00857417⟩