A UNIFIED FORMALISM FOR ACOUSTIC IMAGING TECHNIQUES: ILLUSTRATIONS IN THE FRAME OF A DIDACTIC NUMERICAL BENCHMARK

The problem of localizing and quantifying acoustic sources from a set of acoustic measurements has been addressed, in the last decades, by a huge number of scientists, from different communities (signal processing, mechanics, physics) and in various application fields (underwater, aero, or vibro acoustics). This led to the production of a substantial amount of literature on the subject, together with the development of many methods, specifically adapted and optimized for each configuration and application field, the variety and sophistication of proposed algorithms being sustained by the constant increase in computational and measurement capabilities. The counterpart of this prolific research is that it is quite tricky to get a clear global scheme of the state of the art. The aim of the present work is to make an attempt in this direction, by proposing a unified formalism for different well known imaging techniques, from identification methods (acoustic holography, equivalent sources, Bayesian focusing, Generalized inverse beamforming...) to beamforming deconvolution approaches (DAMAS, CLEAN). The hypothesis, advantages and pitfalls of each approach will be clearly established from a theoretical point of view, with a particular effort in trying to separate differences in the problem definition (a priori information, main assumptions) and in the algorithms used to find the solution. Some parallels will be drawn with well-known algorithms developed in the field of applied mathematics, linked to compressive sensing, sparse representations or non-negativity constraints. Illustrations of the specificities, similarities and computational costs of each approach will be shown for different source configurations (coherent/incoherent/extended/sparse distributions).