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              <p>Bivariate signals occupy a special place, as they can be processed specifically to take account of their geometric properties. They correspond to two-dimensional waves characterized by their polarization state, which reflects the covariance between the two signal components. The aim of this work is to enable the resolution of inverse restoration problems for bivariate signals to benefit from regularization terms relating not only to the signal itself, but also to the covariance between components. This objective leads us to work with the analytical signal and to consider the presence of a quartic term in the cost function. An optimization problem under linear constraints is formulated. An ADMM method is proposed, involving efficient updating steps. Numerical simulations illustrate the good performance and speed of the proposed method.</p>
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              <p>Les signaux bivariés occupent une place à part car ils permettent un traitement spécifique tenant compte de leurs propriétés géométriques. Ils correspondent aux ondes bidimensionnelles caractérisées par leur état de polarisation qui traduit la covariance entre les deux composantes du signal. Ce travail propose de faire bénéficier la résolution des problèmes inverses de restauration des signaux bivariés de termes de régularisation portant non seulement sur le signal lui-même, mais aussi sur la covariance entre composantes. Cet objectif amène à travailler avec le signal analytique et à considérer la présence d'un terme quartique dans la fonction de coût. Un problème d'optimisation sous contraintes linéaires est formulé. Une méthode ADMM est proposée impliquant des étapes de mise à jour efficaces. Les simulations numériques illustrent les bonnes performances et la rapidité de la méthode proposée.</p>
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