Improving resolution and depth of astronomical observations (via modern mathematical methods for image analysis) M. Castellano, D. Ottaviani, A. Fontana,

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 RomaDipartimento di Matematica, “Sapienza” Universita’ di Roma

ADASS XXIVCalgary, Oct 8th 2014

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

Tests on simulated images

F160W (without noise) F160W F160W 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.


F160W (without noise) F160W F160W Texture




F160W (without noise) F160W F160W Structure





Tests on simulated imagesF160W F160W filtered

Standard SExtractor approachon 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

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.



Tests on CANDELS images

CANDELS-DEEP HUDF CANDELS-DEEP DENOISED

Tests on CANDELS images

CANDELS-DEEP HUDF CANDELS-DEEP DENOISED

Super-Resolution

Given a set of “LR frames” with sub-pixel shifts between them we can reconstruct anhigher resolution image

Solution XH

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

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?

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

BACKUP SLIDES

These days: running Sextractor varying all parameters affecting detection (thresholds, background and deblending).


Variational Algorithms for Image decomposition

P-normsL1 p=1, L2 p=2

G-norm

Variational Algorithms for Image decomposition

Image decomposition: optimal splitting parameter

Super-Resolution

Given a set of “LR frames” with sub-pixel shifts between them we can reconstruct anhigher resolution image

Low resolution images XL can be considered as the application of warping (W),

convolution (H) and downsampling (D) operators on the high-res frame XH.

(e.g. Hardie et al. 1998, Zomet & Peleg 2000, Mitzel et al. 2009)


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


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:

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)

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

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

Image Denoising

We can consider an image f as the sum ofa 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

=

+

Documents

Improving resolution and depth of astronomical observations (via modern mathematical methods for image analysis) M. Castellano, D. Ottaviani, A. Fontana,