  Nonlinearity parameter tomography leads to the problem of identifying a
coefficient in a nonlinear wave equation (such as the Westervelt equation)
modeling ultrasound propagation. In this paper we transfer this into frequency
domain, where the Westervelt equation gets replaced by a coupled system of
Helmholtz equations with quadratic nonlinearities. For the case of the
to-be-determined nonlinearity coefficient being a characteristic function of an
unknown, not necessarily connected domain $D$, we devise and test a
reconstruction algorithm based on weighted point source approximations combined
with Newton's method. In a more abstract setting, convergence of a regularised
Newton type method for this inverse problem is proven by verifying a range
invariance condition of the forward operator and establishing injectivity of
its linearisation.
