A Novel, Efficient Algorithm for Subsurface Radar Imaging below a Non-Planar Surface

Abstract

In classical radar imaging, such as in Earth remote sensing, electromagnetic waves are usually assumed to propagate in free space. However, in numerous applications, such as ground penetrating radar or non-destructive testing, this assumption no longer holds. When there is a multi-material background, the subsurface image reconstruction becomes considerably more complex. Imaging can be performed in the spatial domain or, equivalently, in the wavenumber domain (k-space). In subsurface imaging, to date, objects with a non-planar surface are commonly reconstructed in the spatial domain, by the Backprojection algorithm combined with ray tracing, which is computationally demanding. On the other hand, objects with a planar surface can be reconstructed more efficiently in k-space. However, many non-planar surfaces are partly planar. Therefore, in this paper, a novel concept is introduced that makes use of the efficient k-space-based reconstruction algorithms for partly planar scenarios, too. The proposed algorithm forms an image from superposing sub-images where as many image parts as possible are reconstructed in the wavenumber domain, and only as many as necessary are reconstructed in the spatial domain. For this, a segmentation scheme is developed to determine which parts of the image volume can be reconstructed in the wavenumber domain. The novel concept is verified by measurements, both from monostatic synthetic aperture radar data and multiple-input-multiple-output radar data. It is shown that the computational efficiency for imaging irregularly shaped geometries can be significantly augmented when applying the proposed concept.

Keywords: MIMO radar; ground penetrating radar; non-destructive testing; radar; subsurface imaging; synthetic aperture radar.

Figure 1

Subsurface radar imaging scenario: a drone carrying a radar to image subsurface regions below a curved planar ground surface.

Figure 2

Illustration of the refracted optical path from an antenna to a target in a two-layer geometry.

Figure 3

Example geometry sketch for determining the maximum refracted optical path. The incident and refracted angles are denoted α and β, respectively. The lateral dimension is x; the depth dimension is z. The hatched area represents the area to be reconstructed in k-space.

Figure 4

Test setup used for the experiments and sketch of setup with dimensions. A quasi-monostatic SAR illuminates a box filled with sand and four stripes of aluminum foil buried in it (displayed in white in the sketch).

Figure 5

Image reconstruction by proposed hybrid concept (a) and state of the art (Backprojection with ray tracing, (b)).

Figure 6

Employed sparse MIMO array. Transmitters are in red; receivers in blue.

Figure 7

Photographs of measurement setup (left) and test object with dimensions (right).

Figure 8

Segmentation according to the proposed concept. The arrows depict the maximally refracted optical paths at the boundary irregularity. They determine the image area to be reconstructed in k-space (hatched area).

Figure 9

Image reconstruction by segmentation according to boundary parts (a) and proposed concept (b).

Figure 9

Image reconstruction by segmentation according to boundary parts (a) and proposed concept (b).