利用近场数据求解位势反散射问题的直接抽样法

A direct sampling method to an inverse potential scattering problem by near-field data

针对定态Schrdinger方程的位势反散射问题,采用一个直接的抽样方法来重构方程中位势的支集。与一般的抽样法相比,所采用的直接抽样法只需要一个或几个入射方向对应的近场散射数据作为反演数据,并且具有运算简单、对噪声数据不敏感的特点。通过数学推导,从理论上说明:对于二维和三维空间情形,该抽样法都具有可行性和有效性。

For an inverse potential problem of stationary Schrtodinger equation, a direct sampling method is employed to reconstruct the support of the potential. Compared with the general sampling method, the method proposed here only needs the near-field scattered data as measured data corresponding to one or several incident directions, and has the advantages of simple computation and insensitivity to noise. Based on the mathematical derivation, it is theoretically proven that for both two dimension and three dimension cases, this direct sampling method is feasible and efficient.