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)
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