Frequency and noise dependence of the image reconstruction of ground surfaces using the conjugate gradient based algorithm

The ground surface of the Earth is usually mapped using airborne microwave radar. However, it has been shown recently by the author that the Earth's ground surface can also be imaged using radio ground waves with antennas positioned on the ground surface. The image of the surface is obtained by reconstructing the distribution of the normalised surface impedance of the surface from the measurements of the scattered fields at a number of positions around the surface being imaged with electromagnetic radiation from different azimuthal directions. It has also been shown that the inverse problem can be solved iteratively using a conjugate gradient method, and the images of ground surfaces can be produced using the noiseless data of the measured scattered fields at an operating frequency at which the size of the surface is approximately one wavelength. In practice, the image reconstruction depends on the operating frequency, and the measured scattered fields are subject to white noise and measurement errors. The dependence of the image reconstruction using the conjugate gradient method on the operating frequency and noise in the measured data is thus studied and the results of reconstruction errors at different frequencies and signal-to-noise ratios and the reconstructed images are presented. It is shown that the image reconstruction using the conjugate gradient based algorithm has a strong dependence on the operating frequency and noise. However, the algorithm is able to reconstruct the images of ground surfaces in small number of iterations when the signal-to-noise ratio is greater than 12 dB.