Time-domain inverse scattering method for cross-borehole radar imaging

In this paper, we consider a solution method of the inverse problem of imaging two-dimensional (2D) objects buried underground by cross-hole radar data in the time domain. In addition to less information on the targets due to restriction on the arrangement of transmitters and receivers than for full-view cases such as imaging of objects in free space, the large search region between boreholes makes solving the inverse problem difficult. Although iterative optimization approaches take long computing time, these approaches give much better image qualities for high-contrast objects than linear inversions such as a diffraction tomography. However, the reconstruction in a large search region with limited-view measurements often fails trapped in a local minimum. To overcome this difficulty, we propose a two-step iterative approach: the first step is to reduce the search region to a smaller one and the second step is the accurate reconstruction of the targets in the small region. Both steps are based on an iterative optimization approach, i.e., the forward-backward time-stepping method previously proposed. This two-step approach is tested for detection of tunnel-like objects surrounded by a heterogeneous background medium to evaluate its performance. Numerical results indicate the efficiency of the approach and its ability of circumventing local minima.