Through-Wall Imaging With UWB Radar System - KEMT FEI TUKE

2.5 Radar Imaging Methods Overview 31
also very robust in the cases of long synthetic apertures and high squint angles.
It offers the possibility of processing wide-band, low-frequency airborne SAR data
up to near wavelength resolution.
f-k Migration with Ground Surface and Non Loss-Free Compensation
Standard f-k migration assumes that the ground surface is flat and the medium is
loss-free which in reality is not true. Xiaoyin Xu et al. in [146] adapted it to rough
ground surface and lossy medium. When implemented in the Fourier domain, the
wave equation becomes the Helmholtz equation. It is then straight-forward to
incorporate a complex index of refraction in the Helmholtz equation to describe
wave phenomenon in lossy medium [49]. Here the f-k migration is generalized to
the case of rough ground surface and lossy medium. In the framework of Tikhonov
regularization [55], [85], an algorithm was developed that optimally alters the wave
propagation velocity and the complex index of refraction to take into account of
the ground roughness and lossy medium. In the process of searching the optimal
velocity and complex index of refraction, the algorithm is constrained to produce
an image of minimum entropy. By minimizing the entropy of the resulting image,
better results are obtained in terms of enhanced mainlobe, suppressed sidelobes,
and reduced noise.
Prestack Residual f-k Migration
Prestack residual migration in the frequency domain was introduced by Paul C.
Sava in [122]. This method has advantages over classical f-k migration that estimates
interval velocity functions for depth migration. It is more accurate than
methods which are based on focusing the stack of migrated images, so it provides a
more accurate estimate of the correct migration velocities. Although the theory is
developed assuming constant velocity, the method can be used for depth migrated
images produced with smoothly varying velocity models, since the residually migrated
images depend only on the ratio of the reference and updated velocities.
f-k Migration with Anti-Leakage Fourier Transform
This method was introduced by Sheng Xu et al. in [145] in 2004. Its aim is
to estimate the spatial frequency content on an irregularly sampled grid. After
obtaining the Fourier coefficients, the data can be reconstructed on any desired
grid. For this type of transform, difficulties arise from the non-orthogonality of
the global basis functions on an irregular grid. As a consequence, energy from one
Fourier coefficient leaks onto other coefficients. This well-known phenomenon is
called ”spectral leakage”. The key to resolve the spectral leakage is to reduce the
leakages among Fourier coefficients in the original data before the calculation of