ECE 6364 Spring 2009 HW 12 Due 5/4
Problem 1.
In the derivation of the Wiener filter for restoring a continuous image under the continuous/continuous model,
show that
),(),(),( *vuSvuHvuS fffg =
Problem 2.
In the derivation of the Wiener filter for restoring a continuous image under the continuous/continuous model,
show that
),(),(),(),( 2vuSvuHvuSvuS nn
ff
gg +=
Problem 3.
An observed image ),( yxg is modeled as having been formed from a non-zero-mean image ),( yxu that has been
degraded by motion-blur and additive zero-mean white noise n(x,y) with
{}
),(),(cov),(),( 2
βγδαβγβγ
−−==−− yxyxnyxnE naccording to
),(),(
1
),(
0
yxndtyvtxu
T
yxg T
+−= ∫
If the mean ),( yxu of ),( yxu is known, and the covariance ),(cov
β
γ
uof ),( yxu is modeled as stationary
()
[]
yx
u+−= 05.0exp),(cov 2
σβγ
find the Fourier Transform ),( 21
ζ
ζ
M of the Wiener-filter shift-invariant impulse response ),( yxm for restoring
),( yxu from ),( yxg .
Problem 4.
Let uQ
r
r
=
ε
where u
r is a row-ordered unknown image,Qis a known non-singular matrix with inverse 1−
Q, and
ε
r is a zero-mean vector of i.i.d. white noise with variance 2
σ
so that covariance(
ε
r
) = I
2
σ
. You observe a row-
ordered degraded image nuH r
rr +=vwhere n
r is a zero-mean noise vector with covariance matrix I
γ
and u
r
and
n
r are uncorrelated. Find the Discrete Wiener filter for restoring u
r
from v
r
.
Problem 5.
Problem 8.7 -Jain