Acoustic holography and holophony, wave field synthesis and active noise control are based on common elements which are causality, model, objective, and regularization. In the frequency domain (putting causality aside), a simple formulation states the influence - not the interaction - of errors of the model and objective and of regularization of the results. However, it does not give either an understanding or any relation of cause to effect. When the objective can be reached using the available model, regularization is not needed and the information liable to be extracted from this determined problem is poor, unlike in the over-determined case when the model does not allow the objective to be reached. The geometrical interpretation of the over-determined problem written in the least-mean square sense could be a tool to enlighten the influences and interactions in question. After having shown the interest of the geometrical interpretation, a pseudo-analytical inverse problem in spherical holophony and a numerical problem in plane holography provide particular illustrations. From among the properties accessible, one is highlighted: in the case of a perfect objective but inaccurate model, its adaptation brings a decrease in the amount of regularization required and an improvement in the results.
inverse problems; regularization; acoustics
