  We consider an acoustic obstacle reconstruction problem with Poisson data.
Due to the stochastic nature of the data, we tackle this problem in the
framework of Bayesian inversion. The unknown obstacle is parameterized in its
angular form. The prior for the parameterized unknown plays key role in the
Bayes reconstruction algorithm. The most popular used prior is the Gaussian.
Under the Gaussian prior assumption, we further suppose that the unknown
satisfies the total variation prior. With the hybrid prior, the well-posedness
of the posterior distribution is discussed. The numerical examples verify the
effectiveness of the proposed algorithm.
