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

2.5 Radar Imaging Methods Overview 37
from Iw(X, Y, Z) space to the real Ir(x, y, z) space can be done by:
x = X −
Z 2 − d 2 +
�
2Z 3 Zx
(Z 2 − d 2 ) 2 + 4d 2 Z 2 Z 2 X
y = Y + ZY
� 2 2 4
d (x − X) − Z � /Z 3
�
z = Z2 − d2 − (y − Y ) 2 − (Z2 − d2 ) (x − X) 2 /Z 2
(2.5.56)
where d is distance between transmitter and receiver.
SEABED method was used for detecting the contours of object behind a
wooden wall by Sebastian Hantscher et al. in [68] in 2006. The results from
real measurement are compared with Kirchhoff migration and f-k migration on a
very simple scenario. The cylinder was positioned behind the wooden wall with
the smooth surface. The next practical 3 Dimensional (3D) measurement was
done through the 5 cm concrete wall [69] in 2008. The SEABED reasonable saves
a computational time. It is even ten times faster than f-k migration. A number of
points with nonzero amplitudes in Iw(X, Y, Z) space is very small, therefore only
a few points have to be processed. However, for practical scenarios through thick
brick, or concrete walls the derivation of the wave front from the measured data
will be a critical step.
2.5.12 Fast Back Projection
Fast back projection algorithm was developed for tomography [21, 148] and later
modified for airplane SAR imaging in [144]. The main advantage of this method is
the smaller computational complexity in comparison with classical back-projection
described in Section 2.5.2. Classical back projection requires O(N 3 ) operations to
generate N projections for N × N image whereas the fast back projection requires
only O (N 2 log N) operations. The fast back projection algorithm is performed
in two parts. First, the received data are recursively factorised into a number
of decimated data-sets for subimages of the reconstructed image. An example
of factorisation is shown on Fig. 2.5.7 (upper side), the resultant hierarchy of
data-sets is shown on lower side.
Secondly, each data-set is back-projected to the corresponding subimage. A
computational gain is achieved through decimating the data in the factorisation
step. However, this step introduces an error that degrades the image quality
[73]. There were made lot of modifications in the fast projection algorithm, like
filtered back-projection [15], fast factorised back-projection [50], [140], quadtree
back projection [97], omega-k quadtree back projection [36], etc. However, none
of these methods has better accuracy than classical back projection, or faster
computational times than f-k migration.