1. The Wavelet Packets Equalization Technique: Applications on LASCO Images M.Mierla, R. Schwenn, G. Stenborg

2. Contents 1. Motivation 2. Objectives 3. The Data 4. The Wavelet Packets Equalization Technique 5. Applications on LASCO Images 6. Conclusions and Perspectives

3. What are we looking for?  Observational signatures that would allow us to quantify the coronal outflow from regions close to the limb up to larger distances

4. Motivation  Studying the near-sun solar wind; sources and topology  Focusing on the slow solar wind since the fast solar wind is much better known

5.  Unambiguous tracking of the motion of the coronal material  Quantification of such motions Objectives Approach Selective contrast-enhancement of internal structures of both close-to limb features and streamers Temporal correlation of isolated features (HT diagrams)

6. LASCO/SOHO LASCO = Large Angle and Spectrometric COronagraph SOHO = The Solar and Heliospheric Observatory

7. The Data C1 ( LASCO/SOHO) T~2*10 6 K T~2*10 6 K C2 (LASCO/SOHO) white light C3 (LASCO/SOHO) white light Fe XIV

8. The Wavelet Packets Equalization Technique  The technique consists in decomposing a given image in the so called wavelet scales or wavelet planes, the first scales containing the higher (spatial) frequency components and the last ones containing the lower (spatial) frequency signatures.  Wavelet Transform properties allow further decomposition of each wavelet scale in subsequent scales.  By assigning different weight to these levels and subsequently recombining them (plus a smoothed array, called continuum), a very good contrast enhanced image can be obtained. Stenborg & Cobelli, A&A, 2003, in press

9. Wavelet Transform MW: B 3 -spline (1D) The 1D “à trous” algorithm B n -splines (1D) Mother Wavelets Analysis produces a set of resolution- related views of the original signal, called scales. Scaling is achieved by dilating and contracting the basic wavelet to form a set of wavelet functions. Wavelet Scales Starck J.-L. et al., ApJ, 1997

10. The 2D “à trous” algorithmWeight01 15 20 30 40 50 Weight01 15 25 35 45 55Weight01 10 25 30 40 50 Weight01 10 20 35 40 50 Weight01 10 20 30 40 55 original

11. The Wavelet Packets Equalization Technique  The technique consists in decomposing a given image in the so called wavelet scales or wavelet planes, the first scales containing the higher (spatial) frequency components and the last ones containing the lower (spatial) frequency signatures.  Wavelet Transform properties allow further decomposition of each wavelet scale in subsequent scales (wavelet packets).  By assigning different weight to these levels and subsequently recombining them (plus a smoothed array, called continuum), a very good contrast enhanced image can be obtained. Stenborg & Cobelli, A&A, 2003, in press

12. The splitting algorithm A Multiple level wavelet decomposition: w 0 (0) w 1 (0) w 2 (0) w p1 (0)... w k (0) w 0 (0,k) w 1 (0,k) w 2 (0,k) w p2 (0,k)... w m (0,k) w 0 (0,k,m) w 1 (0,k,m) w 2 (0,k,m) w p3 (0,k,m)... w k (0,k,m) I(x,y) Reconstruction: Wickerhauser, 1991 1-D variant  Fligge & Solanki, 1997 (Noise reduction in astronomical spectra) Stenborg & Cobelli, A&A, 2003

13. The Wavelet Packets Equalization Technique  The technique consists in decomposing a given image in the so called wavelet scales or wavelet planes, the first scales containing the higher (spatial) frequency components and the last ones containing the lower (spatial) frequency signatures.  Wavelet Transform properties allow further decomposition of each wavelet scale in subsequent scales.  After noise filtering in the wavelet domain, and assigning different weights to the last level wavelet scales (including the “continuum”) a reconstructed image is obtained, showing selectively contrast- enhanced features. Stenborg & Cobelli, A&A, 2003, in press

14. Noise Progression in Wavelet Space: The Reconstruction Strategy Weighted Reconstruction:  33  03  02  01  00 0  23  13  12  10 1  53  52  51  50 5  43  42  41 4  32  31  30 3  22  21  20 2 3210 Stenborg & Cobelli, A&A, 2003

15. 01…401111 14444 24444 34444 44444 …0000 80000 01…401111 14444 24444 34444 44444 …4444 84444 01…401111 10000 241074 34474 44444 …0000 80000 Original image Fe XIV green line loops in the inner corona as seen by LASCO/C1 on June 01, 1998 at 04:12 UT (upper left). The other frames show three different reconstruction schemes based on an 8 first-level scales plus continuum, each scale further subdivided in 4 scales plus continuum

16. A CME observed by LASCO-C2 coronagraph on August 13, 2002. The upper left image corresponds to the LASCO-C2 raw image with the background removed and the other 3 images correspond to different restoration processes based on an 8 first-level scales plus continuum, each scale further subdivided in 3 scales plus continuum.012300111 10555 20555 30555 40555 …0555 80555 012300000 18888 28888 34444 44444 …4444 84444 Original image012300111 10500 20800 30800 40800 …0800 80800

17. 0123 01111 11111 21111 310101010 45555 …5555 105555 14:41 15:41 LASCO-C3 image recorded on June 2nd, 1998, 15:41 UT. The image corresponds to the LASCO-C3 raw image with the background removed The reconstructed image

18. 14:42 UT15:41 UT16:41 UT 14:42 UT15:41 UT16:41 UT

19. The corona observed by LASCO-C2 coronagraph on August 12-13, 2002. The first movie corresponds to the LASCO-C2 raw images with the background removed and the other 2 movies correspond to different restoration processes based on an 10 first-level scales plus continuum, each scale further subdivided in 3 scales plus continuum.012301111 15555 25555 35555 45555 …5555 105555012301111 10101010 20151515 30151515 40151515 …0101010 100101010 Original images

20. Conclusions  By applying the wavelet packet equalization technique to LASCO images: - diffuse close-to-limb magnetic field structures are better discerned, - diffuse close-to-limb magnetic field structures are better discerned, - faint, small structures, hidden in the background can be revealed, - faint, small structures, hidden in the background can be revealed, - the unseen internal details of coronal transients are revealed. - the unseen internal details of coronal transients are revealed. What do we need this for?

21. LASCO images time I R PA R m Perspectives

22. C2/LASCO, 3 June 1998, 23:57 UT Polar coordinates 100 200 300 123.4 2 4 1 3 5 (Solar radii) 3.9 solar radii Radial distance Angular distance from the equator in west limb

23. END

24. The 2D “à trous” algorithmWeight01 10 25 30 40 50

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28. ReconstructionWeight01 15 25 35 45 55

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32. 012301111 1515107 231075 31753 41531 50311 012301111 10013 21135 31357 435710 5571015

33. - Splines: piecewise polynomials - Spline degree n: each segment is a polynomial of degree n (n+1 coef needed). Additional smoothness constraint: continuity of the spline and derivatives until order n-1. - B splines: basic atoms by which splines are constructed - B 3 minimum curvature property. Why B 3 splines as mother wavelets?

34. A succession of LASCO-C3 images recorded on June 2 nd, 1998. The first column corresponds to the LASCO-C3 raw images with the background removed and the last column corresponds to:012301111 11111 21111 310101010 45555 …5555 105555