IMAGE UNMIXING SUCCESS ESTIMATION IN SPATIALLY VARYING SYSTEMS Ron Gaizman and Yehoshua Y. Zeevi, Department of Electrical Engineering, Technion, Haifa, Israel. 1
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IMAGE UNMIXING SUCCESS ESTIMATION IN
SPATIALLY VARYING SYSTEMS
Ron Gaizman and Yehoshua Y. Zeevi,Department of Electrical Engineering, Technion,
Haifa, Israel.
1
• The problem of recovering source signals from mixtures with only limited knowledge of the mixing process.
• Motivation: Speech signals separation, Image reflection unmixing, Medical Signals Anaysis (MRI, ECG), Communication signals unmixing,…
• Example: “Cocktail party problem”
Introduction
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2
Introduction
1 111 12
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3
Introduction
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21 11 22 122 2
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4
1 11 1
2 12 2
'
'
s h s
s h s
SSCA( Staged Sparse Component Analysis )
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2 2
1 1
2 3
Z SH
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z s
s1
s2
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z2
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s2
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Space invariant Instantaneous example:
Stage 1:Estimate based on sparseness of the data.
Stage 2:Use in order to estimate .H S
H
R.Kaftory, Y.Zeevi 2009
SSCA( Staged Sparse Component Analysis )
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2 3,
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z2
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1000
2000
3000
4000
r1 hist
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
2
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6
r1 smooth by gaussian kernal with =0.040241
| 2.9996| 2.00176
Stage 1:
Non-Sparse signals Sparsify
7
Signals Estimation
8
ˆ
ˆˆ ˆ ˆargmin RegS
S Z H S S
Success Estimation Method (SEM)
* Function Demands:
- Local Minima when
- Smooth, Convex around true parameters.
* Known Methods demand prior knowledge :
- Signals independence on one another ( ).
- Signals sparseness on some domain.
( ) 0.20.3
ˆ ˆ ˆ ˆ, , ,i i i iPC s Edge s Grad s SIFT s
ˆS
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ˆ ˆ ˆ ˆ ˆ: minS S
9
1 2ˆ ˆ,MI s s
A.Achtenberg Thesis 2011
Proposed Success Estimation Method(SEM)
Use additional knowledge of active set coefficients to estimate success.
10
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1 2
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ˆ
ˆ
ˆp p
active set s
active set s
s s z z active set s active set s
z s
z s
1z 1z
11
Proposed Success Estimation Method
Success Estimation Methods (SEM)
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- Success versus deviation in mixing system parameters estimation.- Other methods do not satisfy function demands.
Proposed SEM
Feedback Approach to Signal Estimation
Sparse Representation
System Model Estimation
Sources Estimation
Separation Success
Estimation
Mixtures S
ˆ
ˆ
ˆ ˆmin
ˆ ˆ ˆ ˆ. . argmin RegS
S
s t S Z H S S
13
ˆ
Feedback Approach : An Example
s1
s2
z1
z2
14
s1 gal (lsqlin),MSE=0.00026189, SNR=12.1468[dB]
s2 gal (lsqlin),MSE=0.00023082, SNR=12.4588[dB]
s1 gal-s
1
s2 gal-s
2
Original Signals Mixtures Estimated Signals using SSCA
15
Optimization of success estimation function.
-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2
-0.2
-0.1
0
0.1
0.2
0.1
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0.2
0.25
0.3
0.35
2
1
Success Optimization using Q Newton
Success E
st
Feedback Approach : An Example
ˆ
ˆ
ˆ ˆmin
ˆ ˆ ˆ ˆ. . argmin RegS
S
s t S Z H S S
Feedback Approach : An Example
Without Feedback With Feedback
Summary
• Staged Sparse Component Analysis Method.
• Success Estimation Method For Signal and Image un-mixing.
• Feedback Approach for improving Sources Reconstruction.
17
The End…
18
Mixing kernels
• Instantaneous time/space invariant
• Instantaneous time/space variant
• Attenuation and shift time/space variant
,ij ij ijh a T
,ij ijh a
,ij ijh a
19
Sparsification
• Commutative
• One ‘Active’ Source
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: 1.. , 1.. :
,
z
ii N
s z
i ij j
activeset min z th
activeset j N N
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20
Proposed Success Estimation Method
21
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1 1,
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1 2,
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1,
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1..2
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Single path mixtures
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, , , , , ,x y
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j j
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22
𝑇𝑖𝑗 𝜉
Not Sparse ? Sparsify
23
• Single path spatial distortion system
-> SIFT (for spatial transform)
Model 1 matches:314 (/469) SIFT matches
Model 2 matches:73 (/469) SIFT matches
1...|
|
z
aligned
ii N
aligned
i
i
activeset min z th
activeset z th
Not Sparse ? Sparsify
24
• Single path spatial distortion system
-> SIFT (for spatial transform) + Alignment
z1
z2 aligned
Not Sparse ? Sparsify
25
• Single path spatial distortion system
-> SIFT (for spatial transform) + Alignment + Wavelet Transform (For attenuation model)
50
100
150
200
250
300
350
400
450
500
50 100 150 200 250 300 350 400 450 500
#points=9511
X
Y
100200
300400
50050 100 150 200 250 300 350 400 450 500
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
Y
X
All Points: #= 9579
r
Outliers, #points=5489
Model #1 #points=4090
Estimated Model #1
True Model #1
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