1. Improving resolution and depth of astronomical observations (via modern mathematical methods for image analysis) M. Castellano, D. Ottaviani, A. Fontana, E. Merlin, S. Pilo, M. Falcone INAF- Osservatorio Astronomico di Roma Dipartimento di Matematica, “Sapienza” Universita’ di Roma ADASS XXIV Calgary, Oct 8 th 2014

2. Image decomposition/denoising original + gaussian noise We can consider an image f as the sum of a structural part (u, large details with “regular” properties) plus a texture part (v, e.g. the “noise”). It can be shown that the two can be separated by means of “Total Variation” techniques (e.g. Rudin, Osher & Fatemi 1992). Techniques based on L1, L2 and “G” norms from Aujol et al. IJCV 2006 implemented in a C++ code Astro-Total Variation Denoiser (ATVD) “Structure” “Texture” ATVD

3. Tests on simulated images F160W (without noise)F160WF160W Structure TV-L2 and TVG most effective in removing noise We can test SExtractor detection varying all relevant parameters (thresholds, background and deblending).  number of recovered sources, % spurious detection (on negative image too), completeness levels etc on original and denoised image.

4. Tests on simulated images F160W (without noise)F160WF160W Texture TV-L2 and TVG most effective in removing noise We can test SExtractor detection varying all relevant parameters (thresholds, background and deblending).  number of recovered sources, % spurious detection (on negative image too), completeness levels etc on original and denoised image.

5. F160W (without noise)F160WF160W Structure Tests on simulated images TV-L2 and TVG most effective in removing noise We can test SExtractor detection varying all relevant parameters (thresholds, background and deblending).  number of recovered sources, % spurious detection (on negative image too), completeness levels etc on original and denoised image.

7. Tests on simulated images F160WF160W filtered Standard SExtractor approach on a noisy image: filtering to reduce the noise. Without filtering too many spurious sources are detected… Can we use an (unfiltered) Structure mosaic as detection image in place of the filtered noisy mosaic? Segmentation images

8. Source extraction on the Structure component yields to an higher purity of the catalogue at a similar completeness. Or to a much higher completeness with similar contamination levels.

9. Source extraction on the Structure component yields to an higher purity of the catalogue at a similar completeness. Or to a much higher completeness with similar contamination levels.

10. Source extraction on the Structure component yields to an higher purity of the catalogue at a similar completeness. Or to a much higher completeness with similar contamination levels.

11. Tests on CANDELS images CANDELS-DEEP HUDF CANDELS-DEEP DENOISED

12. Tests on CANDELS images CANDELS-DEEP HUDF CANDELS-DEEP DENOISED

13. Super-Resolution Given a set of “LR frames” with sub-pixel shifts between them we can reconstruct an higher resolution image Solution X H found by minimization of an energy function (requires regularization) Techniques based on L1 and L2 regularization from Unger+ 2010 and Zomet&Peleg 2002 implemented in FORTRAN 90 code SuperResolve

14. Super-Resolution of EUCLID imaging EUCLID will observe >15000 sq. deg. with VIS imager (1 filter@550-900nm): pixel-scale=0.1”, PSF- FWHM~0.18” NIR imager (Y,J,H filters) : pixel-scale=0.3”, PSF-FWHM~0.3” Can Super-Resolution help us in matching NIR to VIS resolutions?

15. Conclusions and future plans Super-Resolution: -Effective at producing higher-res and better sampled images -Ongoing tests of relative advantages w.r.t interpolation, drizzling etc. -Potential application in EUCLID: matching of VIS and NIR resolution. Image decomposition/denoising: -Effective at increasing depth: higher completeness and purity of source detection -Ongoing work on denoising the deep fields (CANDELS fields, HUDF etc) -Potential application in EUCLID: characterization of bright sources (WL), increased number of faint sources for legacy science Planned release of dedicated codes (ATVD, SuperResolve) after ending test phase

17. BACKUP SLIDES

19. These days: running Sextractor varying all parameters affecting detection (thresholds, background and deblending).  number of recovered sources, % spurious detection (on negative image too), completeness levels etc on original and denoised image.

20. Variational Algorithms for Image decomposition

21. P-norms L1  p=1, L2  p=2 G-norm Variational Algorithms for Image decomposition

22. Image decomposition: optimal splitting parameter

23. Super-Resolution Given a set of “LR frames” with sub-pixel shifts between them we can reconstruct an higher resolution image Low resolution images X L can be considered as the application of warping (W), convolution (H) and downsampling (D) operators on the high-res frame X H. (e.g. Hardie et al. 1998, Zomet & Peleg 2000, Mitzel et al. 2009)

24. Super-Resolution of EUCLID imaging EUCLID will observe >15000 sq. deg. with VIS imager (1 filter@550-900nm): pixel-scale=0.1”, PSF-FWHM~0.18” NIR imager (Y,J,H filters) : pixel-scale=0.3”, PSF-FWHM~0.3” Can Super-Resolution help us in matching NIR to VIS resolutions? We can try to use NIR single-epoch frames to build a super-resolved NIR mosaic instead of a standard “coadded” one

25. Super-Resolution of EUCLID imaging

26. Variational Algorithms for image SR (1) Regularization term given by the L2 norm of the image (e.g. Mitzel et al. 2009, Zomet&Peleg 2000, Hardie et al. 1998) It's a convex function, the minimum is given by the condition: Steepest descent minimization: With step:

27. Regularization term given by the L1 norm of the image (Unger et al. 2010). (“edge-preserving” properties) Based on the Huber (1980) norm: with: MAD=”mean absolute deviation”=median(x-median(x)) Variational Algorithms for image SR (2)

28. Different approaches: - Fourier-based techniques (Tsai&Huang 1984) - Variational methods (e.g. Hardie et al. 1998, Mitzel et al. 2009) - Bayesian approaches (e.g. Pickup et al. 2009) - “Example-based” and “image hallucination” approaches (e.g. Datsenko&Elad 2007, Glasner et al. 2009). Overview of Super-Resolution techniques

29. Can we increase HUDF depth!? B435 Y105 J125 H160 Sources detected on H160-denoised, but not present in the CANDELS catalogue: confirmed by detection in other bands

30. Image Denoising We can consider an image f as the sum of a structural part (u, with “regular” properties) plus a texture part (v, e.g. the “noise”). It can be shown that the two can be separated by means of “Total Variation” techniques (e.g. Rudin, Osher & Fatemi 1992) Reference simulated image w/o noise = +