afosr program review:
DESCRIPTION
AFOSR PROGRAM REVIEW:. INNOVATIVE SIGNAL PROCESSING FOR MILITARY DIGITAL COMMUNICATION DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF VERMONT JUNE 6 – 8, 2002. Applications of Finite Group Theory to Signal Processing. by Richard Foote, Gagan Mirchandani and Dan Rockmore. - PowerPoint PPT PresentationTRANSCRIPT
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AFOSR PROGRAM REVIEW:INNOVATIVE SIGNAL
PROCESSING FOR MILITARY DIGITAL COMMUNICATION
DEPARTMENT OF MATHEMATICS AND STATISTICS
UNIVERSITY OF VERMONT
JUNE 6 – 8, 2002
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Applications of Finite Group Theory to Signal Processing
by Richard Foote,
Gagan Mirchandani and
Dan Rockmore
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Finite groups acting on discrete signals
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Wreath products of cyclic groups
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The quadtree X(1,9) with 9 levels
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Group-based image processing
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Multiresolution analysis, filter banks and discrete wavelets
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Example
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Current research directions
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2. APPLICATIONS WITH WPC GROUPS
1. WPT – 4-channel PR FB
2. WPT extensions
3. WPT phase – implications
4. WPT applications
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1 1 1 1
1 -j -1 j
1 j -1 -j
1 -1 1 -14
4
1 1 1 1
1 -j -1 j
1 j -1 -j
1 -1 1 -1
4
4
4
4
4
4
X[n]X[n-3]
4-channel PR FB (complex)
Orthogonal,linear phaseShort delayGroup invariantShiftableFast transform, integer arithmeticPhase available
Not very regularNot translation invariant
2
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WPT Extensions - 2D WPT
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x1
2
0
3
x
xx
WPT phase – a gradient estimate
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23x
xx01
x1
x2
x3
x 1-D DFT
1
2
0
3
V
V V
V
1V
x0
~~
~~
~
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-45
Edges Phase angle
HH
-45
Relationship: Edge angle and WPT phase (V )1 ~
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Spectrum: Angle -45, BW 10
Reconstruction: Angle -45, BW 10
Reconstruction: Angle -80, BW 5
Steerable filtering* with group-based filters
* work with Valerie Chickanosky
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Original V 1
|V | Cos ( )1
θ
~
~α
α
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Reconstruction withglobal phase
Reconstruction withlocal (WPT) phase
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1. Image segmentation
2. Texture classification
3. Motion estimation
4. Overlapped WPT
Other applications of phase
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Acknowledgements
Jun Ge Xuling LuoValerie Chickanosky