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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Introduction

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Introduction

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SSCA( Staged Sparse Component Analysis )

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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

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R.Kaftory, Y.Zeevi 2009

SSCA( Staged Sparse Component Analysis )

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r1 smooth by gaussian kernal with =0.040241

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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

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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.

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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

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13

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Feedback Approach : An Example

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s1 gal (lsqlin),MSE=0.00026189, SNR=12.1468[dB]

s2 gal (lsqlin),MSE=0.00023082, SNR=12.4588[dB]

s1 gal-s

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s2 gal-s

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Original Signals Mixtures Estimated Signals using SSCA

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Optimization of success estimation function.

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Success Optimization using Q Newton

Success E

st

Feedback Approach : An Example

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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

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Sparsification

• Commutative

• One ‘Active’ Source

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Proposed Success Estimation Method

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𝑇𝑖𝑗 𝜉

Not Sparse ? Sparsify

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• 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

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• 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

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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