The Second CTA Pipeline Developer’s...

Introduction Tailcut Wavelets Conclusion References

The Second CTA Pipeline Developer’s WorkshopAdvanced Image Cleaning

Jérémie Decock

CEA Saclay - Irfu/SAp

October 11, 2016

Decock CEA Saclay - Irfu/SAp

The Second CTA Pipeline Developer’s Workshop


Introduction




Introduction

Subject

Try to improve image cleaning before Hilas parametrization

Improve methods to remove:

I Instrumental noise

I Background noise

Motivations:

I Keep more signal (deeper into the noise)

I Reduce threshold

I Maybe eventually do cleaning and time-integration all at once




Current method (HESS)




Description

The “Tailcuts clean” algorithmA very simple cleaning procedure:

I Keep pixels above a given threshold (e.g. 10 PE)

I Keep some neighbors of these selected pixels: those above asecond (lower) threshold (e.g. 5 PE)

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First threshold

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Description

Example

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Input image

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Reference image

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Description

Remarks

I Fast and simple

I Sufficient for bright showers

I But surely we can do better for faint showers




An alternative method




Description

Basic idea

I Tailcut method: threshold in the main space

I Better idea: threshold in a different space where signal andnoise can be easily separated




Description

Wavelet Transform method

Roughly the same idea than doing filtering with Fourier Transform

I Apply the transform on the signal

I Apply a threshold in the transformed space

I Invert the transform to go back to the original signal space

Differences with Fourier Transform

I Use wavelets instead sin and cos functions as new bases in thetransformed space

I The transformed space contains spatial information




Description

Overview

A wavelet looks like this (Morlet):

“A wave-like oscillation with an amplitude that begins at zero,increases, and then decreases back to zero”




Conclusion




Conclusion

Conclusion

This is a work is in progress... We will try to give some first resultsin Bologna Meeting or soon after

Thanks to CosmoStat we have some tools to apply wavelettransforms (”mr transform”)




References I



Appendix

Appendix



Appendix

Noise

ClarificationsDifferent kind of “noise” in telescope images (to be completed...)

1. Instrumental noise (Photomultiplier Tubes, ...)I Thermionic emissionI RadiationsI Electric noise

2. Background noise (Night Sky Background or NSB)I Parasite light (moon, stars, planes, light pollution, ...)



Appendix

Tailcut

The “Tailcuts clean” listing (Python)

1 def tailcuts_clean(geom , image , pedvars ,

picture_thresh =4.25, boundary_thresh =2.25):

2

3 clean_mask = image >= picture_thresh * pedvars

4 boundary_mask = image >= boundary_thresh * pedvars

5

6 boundary_ids = []

7 for pix_id in geom.pix_id[boundary_mask ]:

8 if clean_mask[geom.neighbors[pix_id ]]. any():

9 boundary_ids.append(pix_id)

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11 clean_mask[boundary_ids] = True

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13 return clean_mask

listings/tailcuts clean.py



Appendix

FFT

First alternativeDiscrete Fourier Transform method

I Previous filter: threshold in the main space

I Better idea: threshold in a different space where signal andnoise can be easily separated



Appendix

FFT

Fourier transform

f (t) =a02

+∞∑n=1

(an cos(nt) + bn sin(nt))

an =1

π

∫ π−π

f (t) cos(nt)dt

bn =1

π

∫ π−π

f (t) sin(nt)dt

Discrete Fourier Transform (DFT)

Fourier Transform for discrete signals (digital pictures, ...)



Appendix

FFT

Clean signals with DFTRemove noise in direct space: difficult (here)

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4Signal



Appendix

FFT

Clean signals with DFTRemove noise in transformed space: easy (here)

I Apply DFT

I Apply a threshold

I Apply invert DFT

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Fourier coefficients

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Filtred fourier coefficients



Appendix

FFT

Remarks

FFT can be applied to any T -periodic function f verifying theDirichlet conditions:

I f must be continuous

I and monotonic

I on a finite number of sub-intervals (of T )

Signals defined on bounded intervals (e.g. images) can beconsidered as periodic functions (applying infinite repetitions)



Appendix

FFT

Analyse

Works well:

I when the Fourier coefficients for the signal and the noise caneasily be separated in the Fourier space (obviously...)

I e.g. when either the signal or the noise can be defined withfew big Fourier coefficients (i.e. signal or noise have a fewnumber of significant harmonics)



IntroductionIntroduction

Current method (HESS)Description

An alternative methodDescription

ConclusionConclusion

AppendixNoiseTailcutFFT

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