Aerospace and Electronic Systems Magazine July 2017 - 43

Lim, Gianelli, and Li
hybrid high-resolution method is applied to image formation, and
compare its output with the BP image in Figure 6. Clearly, the hybrid high-resolution imaging algorithm offers a superior image in
terms of its resolution and sidelobe levels. The hybrid method begins with 9 iterations of SIAA, which yield the preliminary results
followed by one iteration of FIAA to supply accurate and unbiased
images of targets. As a final step, two iterations of SLIM with q →
0 are applied to yield sparsity in the target SAR images.
2-D SIAA operates on J overlapping windows of phase history
data of size S1 × S2, with S1 < M and S2 < Np. The SAR image is
formed by repeating
 −1y j
d H R

βˆ pj =  Hr ,l  −1  ,  j = 1,..., J
d r ,l R d r ,l
r ,l

The quantities with tilde in (9) and (10) are windowed. The initial
j
 =I
estimate of β pr ,l is obtained by using the matched filter with R
j
j
in (9). y = vec Y and Yj is the jth window of mat {y} of size M
⋅ denotes column-wise vectorization and mat {}
⋅
× Np, where vec {}
the inverse operation, recreating the matrix from the vectorized
matrix. As SIAA operates on a subset of the phase history data at
a given time, a substantially computational complexity reduction
is achieved [6].
Following the image initialization by SIAA, FIAA is applied to
obtain more accurate estimates of the pixel reflection coefficient.
The initial covariance matrix R for FIAA is obtained by using the
Φr,l from the final iteration of SIAA. The 2-D FIAA SAR image is
then formed by

{ }

(9)

R

L

R = Φ r ,l d r ,l d rH,l

and

r =1 l =1

R

L

 =
R
Φr ,l d r ,l d rH,l

and
(10)

r =1 l =1

γˆ p =

until the convergence, where
Φ r ,l =

1 J ˆj
 βp
J j =1 r ,l

(12)

r ,l

2

(11)

d rH,l R −1y
d rH,l R −1d r ,l

.

(13)

 −1 in SIAA and R−1 in FIAA are calculated using GohbergThe R
Semencul (GS) factorization [13], [14].
In order to arrive at SAR images with a desirable amount of sparsity,
two iterations of the SLIM algorithm [7] with q → 0 are applied to the

Figure 6.

BP SAR images: full data {(a),(d),(g)}, 30% missing data {(b),(e),(h)} and 50% missing data {(c),(f),(i)}. Each image is in 5m by 5m and 0.05m pixel
size.

JULY 2017

IEEE A&E SYSTEMS MAGAZINE

43



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