Towards a Robust Imprecise Linear Deconvolution

Deconvolution consists of reconstructing a signal from blurred (and usually noisy) sensory observations. It requires perfect knowledge of the impulse response of the sensor. Relevant works in the litterature propose methods with improved precision and robustness. But those methods are not able to account for a partial knowledge of the impulse response of the sensor. In this article, we experimentally show that inverting a Choquet capacity-based model of an imprecise knowledge of this impulse response allows to robustly recover the measured signal. The method we use is an interval valued extension of the well known Schultz procedure.