Image Processing Reference
In-Depth Information
1
Where
K
= (
SR S
+
A
-1
)
-1
(18)
represents the robustified reconstruction operator for the uncertain scenario.
2.3.3 DEDR imaging techniques
In this sub-section, three practically motivated DEDR-related imaging techniques
(Shkvarko, 2008) are presented that will be used at the HW co-design stage, namely, the
conventional matched spatial filtering (MSF) method, and two high-resolution
reconstructive imaging techniques: (i) the robust spatial filtering (RSF), and (ii) the robust
adaptive spatial filtering (RASF) methods.
1.
MSF
: The MSF algorithm is a member of the DEDR-related family specified for
>>
||
S
+
S
||, i.e. the case of a dominating priority of suppression of noise over the
systematic error in the optimization problem (7). In this case, the SO (9) is approximated
by the matched spatial filter (MSF):
F
MSF
= F
(1)
S
+
.
(19)
2.
RSF
: The RSF method implies no preference to any prior model information (i.e.,
A
=
I
)
and balanced minimization of the systematic and noise error measures in (14) by
adjusting the regularization parameter to the inverse of the signal-to-noise ratio (SNR),
e.g.
=
N
0
/
B
0
, where
B
0
is the prior average gray level of the image. In that case the SO
F
becomes the Tikhonov-type robust spatial filter
F
RSF
=
F
(2)
= (
S
+
S
+
RSF
I
)
-1
S
+
.
(20)
in which the RSF regularization parameter
RSF
is adjusted to a particular operational
scenario model, namely,
RSF
= (
N
0
/
b
0
) for the case of a certain operational scenario, and
RSF
= (
N
/
b
0
) in the uncertain operational scenario case, respectively, where
N
0
represents the white observation noise power density,
b
0
is the average a priori SSP
value, and
N
=
N
0
+ corresponds to the augmented noise power density in the
correlation matrix specified by (16).
3.
RASF
: In the statistically optimal problem treatment, and
A
are adjusted in an
adaptive fashion following the minimum risk strategy, i.e.
A
-1
=
D
= diag(
b
), the
diagonal matrix with the estimate
b
at its principal diagonal, in which case the SOs (9),
(17) become itself solution-dependent operators that result in the following robust
adaptive spatial filters (RASFs):
ˆ
n
1
11
n
1
F
RASF
=
F
(3)
=
(
SR S
+
D
SR
(21)
for the certain operational scenario, and
ˆ
1
11
1
F
RASF
= F
(4)
= (
SR S
+
D
SR
(22)
for the uncertain operational scenario, respectively.
Using the defined above SOs, the DEDR-related data processing techniques in the
conventional pixel-frame format can be unified now as follows
B
=
L
{
b
} =
L
{{
F
(
p
)
YF
(
p
)+
}
diag
}; );
p
= 1, 2, 3, 4
(23)