S.Klimenko, December 2003, GWDAW Burst detection method in wavelet domain (WaveBurst) S.Klimenko,...
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Transcript of S.Klimenko, December 2003, GWDAW Burst detection method in wavelet domain (WaveBurst) S.Klimenko,...
![Page 1: S.Klimenko, December 2003, GWDAW Burst detection method in wavelet domain (WaveBurst) S.Klimenko, G.Mitselmakher University of Florida l Wavelets l Time-Frequency.](https://reader035.fdocuments.us/reader035/viewer/2022070610/5a4d1b947f8b9ab0599c2c84/html5/thumbnails/1.jpg)
S.Klimenko, December 2003, GWDAW
Burst detection method in wavelet domain
(WaveBurst)
S.Klimenko, G.Mitselmakher
University of Florida Wavelets Time-Frequency analysis Coincidence Statistical approach Summary
![Page 2: S.Klimenko, December 2003, GWDAW Burst detection method in wavelet domain (WaveBurst) S.Klimenko, G.Mitselmakher University of Florida l Wavelets l Time-Frequency.](https://reader035.fdocuments.us/reader035/viewer/2022070610/5a4d1b947f8b9ab0599c2c84/html5/thumbnails/2.jpg)
S.Klimenko, December 2003, GWDAW
Wavelet basis
Daubechies
basis t bank of template waveforms 0 -mother wavelet a=2 – stationary wavelet
Fourier
wavelet - natural basis for burstsfewer functions are used for signal approximation – closer to match filter
ktaa jjjk 0
2/
notlocal
Haar localorthogonalnot smooth
local, smooth,
notorthogonal
MarrMexicanhat local
orthogonalsmooth
![Page 3: S.Klimenko, December 2003, GWDAW Burst detection method in wavelet domain (WaveBurst) S.Klimenko, G.Mitselmakher University of Florida l Wavelets l Time-Frequency.](https://reader035.fdocuments.us/reader035/viewer/2022070610/5a4d1b947f8b9ab0599c2c84/html5/thumbnails/3.jpg)
S.Klimenko, December 2003, GWDAW
Wavelet Transform decomposition in basis {(t)}
d4
d3
d2
d1
d0
aa. wavelet transform tree b. wavelet transform binary tree
d0
d1
d2
a
dyadic linear
time-scale(frequency) spectrograms
critically sampledDWT
fxt=0.5 LP HP
![Page 4: S.Klimenko, December 2003, GWDAW Burst detection method in wavelet domain (WaveBurst) S.Klimenko, G.Mitselmakher University of Florida l Wavelets l Time-Frequency.](https://reader035.fdocuments.us/reader035/viewer/2022070610/5a4d1b947f8b9ab0599c2c84/html5/thumbnails/4.jpg)
S.Klimenko, December 2003, GWDAW
TF resolution
d0
d1
d2
depend on what nodes are selected for analysis dyadic – wavelet functions constant variable multi-resolution select significant pixels
searching over all nodes and “combine” them into clusters.
wavelet packet – linear combinationof wavelet functions
![Page 5: S.Klimenko, December 2003, GWDAW Burst detection method in wavelet domain (WaveBurst) S.Klimenko, G.Mitselmakher University of Florida l Wavelets l Time-Frequency.](https://reader035.fdocuments.us/reader035/viewer/2022070610/5a4d1b947f8b9ab0599c2c84/html5/thumbnails/5.jpg)
S.Klimenko, December 2003, GWDAW
Choice of Wavelet
Wavelet “time-scale” plane
wavelet resolution: 64 Hz X 1/128 secSymlet Daubechies Biorthogonal
=1 ms
=100 ms
sg850Hz
![Page 6: S.Klimenko, December 2003, GWDAW Burst detection method in wavelet domain (WaveBurst) S.Klimenko, G.Mitselmakher University of Florida l Wavelets l Time-Frequency.](https://reader035.fdocuments.us/reader035/viewer/2022070610/5a4d1b947f8b9ab0599c2c84/html5/thumbnails/6.jpg)
S.Klimenko, December 2003, GWDAW
burst analysis methoddetection of excess power in wavelet domain
use waveletsflexible tiling of the TF-plane by using wavelet
packetsvariety of basis waveforms for bursts
approximation low spectral leakagewavelets in DMT, LAL, LDAS: Haar, Daubechies,
Symlet, Biorthogonal, Meyers. use rank statistics
calculated for each wavelet scale robust
use local T-F coincidence rulesworks for 2 and more interferometerscoincidence at pixel level applied before triggers
are produced
![Page 7: S.Klimenko, December 2003, GWDAW Burst detection method in wavelet domain (WaveBurst) S.Klimenko, G.Mitselmakher University of Florida l Wavelets l Time-Frequency.](https://reader035.fdocuments.us/reader035/viewer/2022070610/5a4d1b947f8b9ab0599c2c84/html5/thumbnails/7.jpg)
S.Klimenko, December 2003, GWDAW
“coincidence”
Analysis pipeline
bpselection of loudest (black) pixels (black pixel probability P~10% - 1.64 GN rms)
wavelet transform,data conditioning,
rank statistics
channel 1
IFO1 cluster generation
bp
wavelet transform,data conditioning
rank statistics
channel 2
IFO2 cluster generation
bp“coincidence”
wavelet transform,data conditioning
rank statistics
channel 3,…
IFO3 cluster generation
bp“coincidence”
![Page 8: S.Klimenko, December 2003, GWDAW Burst detection method in wavelet domain (WaveBurst) S.Klimenko, G.Mitselmakher University of Florida l Wavelets l Time-Frequency.](https://reader035.fdocuments.us/reader035/viewer/2022070610/5a4d1b947f8b9ab0599c2c84/html5/thumbnails/8.jpg)
S.Klimenko, December 2003, GWDAW
Coincidence
accept
Given local occupancy P(t,f) in each channel, after coincidence the black pixel occupancy is
for example if P=10%, average occupancy after coincidence is 1%
can use various coincidence policies allows customization of the pipeline for specific burst searches.
),(),( 2 ftPftPC
reject
no pixelsor
L<threshold
![Page 9: S.Klimenko, December 2003, GWDAW Burst detection method in wavelet domain (WaveBurst) S.Klimenko, G.Mitselmakher University of Florida l Wavelets l Time-Frequency.](https://reader035.fdocuments.us/reader035/viewer/2022070610/5a4d1b947f8b9ab0599c2c84/html5/thumbnails/9.jpg)
S.Klimenko, December 2003, GWDAW
Cluster Analysis (independent for each IFO)
Cluster Parameters
size – number of pixels in the corevolume – total number of pixelsdensity – size/volumeamplitude – maximum amplitudepower - wavelet amplitude/noise rmsenergy - power x sizeasymmetry – (#positive - #negative)/sizeconfidence – cluster confidenceneighbors – total number of neighborsfrequency - core minimal frequency [Hz]band - frequency band of the core
[Hz]time - GPS time of the core
beginningduration - core duration in time [sec]
cluster corepositive negative
cluster halo
cluster T-F plot area with high occupancy
![Page 10: S.Klimenko, December 2003, GWDAW Burst detection method in wavelet domain (WaveBurst) S.Klimenko, G.Mitselmakher University of Florida l Wavelets l Time-Frequency.](https://reader035.fdocuments.us/reader035/viewer/2022070610/5a4d1b947f8b9ab0599c2c84/html5/thumbnails/10.jpg)
S.Klimenko, December 2003, GWDAW
Statistical Approach statistics of pixels & clusters
(triggers) parametric
Gaussian noise pixels are statistically independent
non-parametric pixels are statistically independent based on rank statistics:
iii xuRy )( – some functionu – sign function
data: {xi}: |xk1| < | xk2| < … < |xkn|rank: {Ri}: n n-1 1
example: Van der Waerden transform, RG(0,1)
![Page 11: S.Klimenko, December 2003, GWDAW Burst detection method in wavelet domain (WaveBurst) S.Klimenko, G.Mitselmakher University of Florida l Wavelets l Time-Frequency.](https://reader035.fdocuments.us/reader035/viewer/2022070610/5a4d1b947f8b9ab0599c2c84/html5/thumbnails/11.jpg)
S.Klimenko, December 2003, GWDAW
non-parametric pixel statistics
calculate pixel likelihood from its rank:
Derived from rank statistics non-parametric
likelihood pdf - exponential
iii x
nPRy uln
nPRixi
percentile probability
![Page 12: S.Klimenko, December 2003, GWDAW Burst detection method in wavelet domain (WaveBurst) S.Klimenko, G.Mitselmakher University of Florida l Wavelets l Time-Frequency.](https://reader035.fdocuments.us/reader035/viewer/2022070610/5a4d1b947f8b9ab0599c2c84/html5/thumbnails/12.jpg)
S.Klimenko, December 2003, GWDAW
statistics of filter noise (non-parametric)
non-parametric cluster likelihood
sum of k (statistically independent) pixels has gamma distribution
)()(
1
keYYpdf
kYkk
k
k
ii
k nPRY
0ln
P=10%
y
single pixel likelihood
![Page 13: S.Klimenko, December 2003, GWDAW Burst detection method in wavelet domain (WaveBurst) S.Klimenko, G.Mitselmakher University of Florida l Wavelets l Time-Frequency.](https://reader035.fdocuments.us/reader035/viewer/2022070610/5a4d1b947f8b9ab0599c2c84/html5/thumbnails/13.jpg)
S.Klimenko, December 2003, GWDAW
statistics of filter noise (parametric)
,2
22
pxxy
,)( yeypdf
121 px
P=10%xp=1.64
y
Gaussian noise
x: assume that detector noise is gaussian y: after black pixel selection (|x|>xp)
gaussian tails Yk: sum of k independent pixels distributed
as k
k
ik y0
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S.Klimenko, December 2003, GWDAW
cluster confidence
cluster confidence: C = -ln(survival probability)
pdf(C) is exponential regardless of k.
dxexYC
kY
xkkk
1)(
1ln)(
S2 inj
non-parametric C
para
met
ric C
S2 inj
non-parametric C
para
met
ric C
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S.Klimenko, December 2003, GWDAW
Summary
•A wavelet time-frequency method for detection of un-modeled bursts of GW radiation is presented Allows different scale resolutions and wide
choice of template waveforms.Uses non-parametric statistics
robust operation with non-gaussian detector noise
simple tuning, predictable false alarm rates
Works for multiple interferometersTF coincidence at pixel levellow black pixel threshold