Detection of pollution terms in nonlinear second order wave systems

ABSTRACT

In this article we are concerned by the problem of detection of noisy terms which arise in image processing as for remote sensing problems, and which are modelled by a nonlinear wave hyperbolic equation. Some data are missing, then the sentinel method of J.-L. Lions (1992) is used; it is a particular least square-like method which permits to distinguish between the missing terms and the pollution terms. In particular, the sentinel theory is given here in its more general and more realistic setting for hyperbolic problems: in this case, the observation and the control have their support in different open sets. The problem of finding a sentinel is equivalent to a non classical null-controllability problem for the wave equation that we solve.

Graphical Abstract

Keywords:

• Nonlinear wave equation
• sentinels
• null-controllability
• observability inequality

View correction statement:

Corrigendum

Notes

No potential conflict of interest was reported by the authors.