Copyright, 1996 © Dale Carnegie & Associates, Inc. Image Restoration Hung-Ta Pai Laboratory for...
-
Upload
sheena-sims -
Category
Documents
-
view
213 -
download
0
Transcript of Copyright, 1996 © Dale Carnegie & Associates, Inc. Image Restoration Hung-Ta Pai Laboratory for...
Copyright, 1996 © Dale Carnegie & Associates, Inc.
Image Restoration
Hung-Ta Pai
Laboratory for Image and Video Engineering
Dept. of Electrical and Computer Engineering
The University of Texas at Austin
Austin, TX 78712-1084
Degradation Model
In noise-free cases, a blurred image can be modeled as
image original:x
function blur invariant-space linear : h
h x y
In the DFT domain, Y(u,v) = X(u,v) H(u,v)
Inverse Filtering
Assume h is known (low-pass filter) Inverse filter G(u,v) = 1 / H(u,v) v)G(u, v)Y(u,v)(u,X ~
Least Mean Square Filter
Wiener Filter Formulation
v)(u,v)/S(u,Sv)H(u,
v)(u,H v)G(u,
xn
2
*
In practice
Kv)H(u,
v)(u,H v)G(u,
*
2
Maximum-Likelihood (ML) Estimation
h is unknown
)}|p(y maxarg{ ml
Solution is difficult
Parametric set is estimated by
Assume parametric models for the blur function, original image, and/or noise
Expectation-Maximization (EM) Algorithm
Find complete set : for z , f(z)=y
Expectation-step
Choose an initial guess of
Maximization-step
]y,|)|[p(z)|( kk Eg
)|( max arg k
g1k
Subspace Methods
4
3
2
1
0
210
210
210
2
1
0
432
321
210
a
a
a
a
a
bbb00
0bbb0
00bbb
b
b
b
aaa
aaa
aaa
Observe
Subspace Methods
Several blurred versions of original image are available
Construct a block Hankel matrix of blurred images
= , where is a block Toeplitz matrix of the blur functions and is a block Hankel matrix of the original image
Conclusions
Noise-free case: inverse filtering
Multichannel blind case: subspace methods
Blind case: Maximum-Likelihood approach using the Expectation-Maximization algorithm
Noisy case: Weiner filter