Image Processing Reference
In-Depth Information
The problem of enhanced remote sensing (RS) imaging is stated and treated as an ill-
posed nonlinear inverse problem with model uncertainties. The challenge is to perform
high-resolution reconstruction of the power spatial spectrum pattern (SSP) of the
wavefield scattered from the extended remotely sensed scene via space-time processing of
finite recordings of the RS data distorted in a stochastic uncertain measurement channel.
The SSP is defined as a spatial distribution of the power (i.e. the second-order statistics) of
the random wavefield backscattered from the remotely sensed scene observed through
the integral transform operator (Henderson & Lewis, 1998), (Shkvarko, 2008). Such an
operator is explicitly specified by the employed radar signal modulation and is
traditionally referred to as the signal formation operator (SFO) (Shkvarko, 2006). The
classical imaging with an array radar or SAR implies application of the method called
“matched spatial filtering” to process the recorded data signals (Franceschetti et al., 2006),
(Shkvarko, 2008), (Greco & Gini, 2007). A number of approaches had been proposed to
design the constrained regularization techniques for improving the resolution in the SSP
obtained by ways different from the matched spatial filtering, e.g., (Franceschetti et al.,
2006), (Shkvarko, 2006, 2008), (Greco & Gini, 2007), (Plaza, A. & Chang, 2008), (Castillo
Atoche et al., 2010a, 2010b) but without aggregating the minimum risk descriptive
estimation strategies and specialized hardware architectures via FPGA structures and
VLSI components as accelerators units. In this study, we address a extended descriptive
experiment design regularization (DEDR) approach to treat such uncertain SSP
reconstruction problems that unifies the paradigms of minimum risk nonparametric
spectral estimation, descriptive experiment design and worst-case statistical performance
optimization-based regularization.
2.1 Problem statement
Consider a coherent RS experiment in a random medium and the narrowband assumption
(Henderson & Lewis, 1998), (Shkvarko, 2006) that enables us to model the extended object
backscattered field by imposing its time invariant complex scattering (backscattering)
function
e
(
x
) in the scene domain (scattering surface)
X
x
. The measurement data
wavefield
u
(
y
) =
s
(
y
)
+
n
(
y
)
consists of the echo signals
s
and additive noise
n
and is
available for observations and recordings within the prescribed time-space observation
domain
Y
=
T
P
, where
y
= (
t
,
p
)
T
defines the time-space points in
Y
. The model of the
observation wavefield
u
is defined by specifying the stochastic equation of observation (EO)
of an operator form (Shkvarko, 2008):
u
=
S
+ n
;
e
E;
u, n
U;
S
: E U ,
(1)
in the Hilbert signal spaces E and U with the metric structures induced by the inner
products, [
u
1
,
u
2
]
U
=
uud
() ()
yyy
, and [
e
1
,
e
2
]
E
=
e
() ()
xxx
,
respectively.
The operator
e
d
1
2
1
2
Y
X
model of the stochastic EO in the conventional integral form (Henderson & Lewis, 1998),
(Shkvarko, 2008) may be rewritten as
Se
)(
y
) =
(
y
)
= (
()
S
(
yx
,
)
e
(
x
)
d
x
+4
n
(
y
) =
S
(
yx
e
(
x
)
d
x
+(
,
)
yx
e
(
x
)
d
x
+
n
(
y
) .
,
)
(2)
X
X
X
