Application Of Music-type Imaging In Inverse Scattering

The main idea of inverse acoustic scattering problem is to detect and identify the location and shape of an unknown scatter through the incident wave and scatter data. Traditional approach describes the scatter by Newton iteration method.Nevertheless, without a good initial guess close to the target, we can’t recover the boundary of obstacle. In order to overcome this problem, we study the structure of well-known non-iterative method—Multiple Signal Classification(MUSIC) algori thm. MUSIC imaging techniques are usually adopted for imaging of unknown targets, such as location of small scatters and shapes of crack inclusions. So we will have a further research of MUSIC imaging techniques of regional scatters in this paper.MUISIC algorithm is a discrete numerical method, this paper describes imaging spectral function of impenetrable and penetrable domain scatter.Firstly, we discuss direct acoustic scattering problems. We transfer the outgoing problem of the boundary into Fredholm integral equations which are consist of single-layer and double-layer potentials. Then we get the scatter data by Nystr?m method which discretizes the Fredholm integral equations.Secondly, we discuss direct acoustic scattering problems. With the help of the eigen-decomposition of the far-field matrix, we construct spectral function though the orthogonality of large eigen-matrix and small eigen-matrix. We constuct imaging spectral function in single-frequency and multi-frequency cases and explain the reason that spectral function appears peak on the boundary by Bessel function of integer order of the first kind.Finally, some numerical examples are shown that single and multi-frequency MUSIC algorithm are good at recovering scatters of different boundary. MUSIC algorithm can recover not only two-dimension but also three-dimension scatters.MUSIC algorithm can also reconstruct many scatters.