A Fast Iterative Interpolation Method in f-k Domain for 3-D Irregularly Sampled GPR Data

We propose a new iterative interpolation method for ground penetrating radar (GPR) data based on projection onto convex sets (POCS) and frequency-wavenumber (f-k) zone-pass filtering. The main purpose of this method is to simplify the three-dimensional (3-D) GPR data acquisition; it can also be used for conventional GPR data that include some missing traces. This approach allows the reconstruction of the image from sparsely sampled data that violate the Nyquist criterion. The method can fully use 3-D information and works well with irregularly sampled data. Compared to other iterative interpolation methods, the proposed method needs many fewer iterations and can avoid aliasing. The algorithm is demonstrated with both synthetic data and real GPR measurements from a sand pit experiment. In the latter, the target could still be well reconstructed after 80% of the traces were randomly removed. The average spatial interval of the resampled data was 12 cm, which is much larger than the necessary interval as calculated using the Nyquist criterion. Detailed discussions on the large gap recovery issue and aliasing issue are also provided. The results indicate that it should be possible to reduce the data acquisition density in many GPR applications.