Analysis and Improvement of Direct Sampling Method in the Monostatic Configuration

The recently introduced noniterative imaging method entitled “direct sampling method” (DSM) is known to be fast, robust, and effective for inverse scattering problems in the multistatic configuration but fails when applied to the monostatic one. To the best of our knowledge, no explanation of this failure has been provided yet. Thanks to the framework of the asymptotic and the far-field hypothesis in the 2-D scalar configuration, an analytical expression of the DSM indicator function in terms of the Bessel function of order zero and sizes, shapes, and permittivities of the inhomogeneities is obtained and the theoretical reason of the limitation identified. A modified version of DSM is then proposed in order to improve the imaging method. The theoretical results are supported by numerical results using synthetic data.

I. Introduction

The 2-D inverse scattering problem is an important topic due to potential applications in modern human life, e.g., biomedical imaging [1]–[3], nondestructive evaluation [4]–[6], synthetic aperture radar (SAR) imaging [7]–[10], and ground-penetrating radar (GPR) [11]–[13]. However, because of its inherent nonlinearity and illposedness, it is difficult to solve. Among the various imaging methods, noniterative-type algorithms are of interest due to expected numerical simplicity and low computational cost, for example, MUltiple SIgnal Classification (MUSIC), linear sampling method (LSM), topological derivative, Kirchhoff migration, and direct sampling method (DSM). Related works can be found in [14]–[19] and references therein. Even though these methods can provide good results with multistatic data, they may fail with monostatic ones due to the lack of information arising to great assumption from inherent limitation. However, as the monostatic configuration is encountered in various applications such as GPR and SAR, deep understanding and development of effective algorithms are needed.