# How can I combine my favourite surveys to improve deblending?

Rémy Joseph, Peter Melchior,

Fred Moolekamp

HST cosmos, F814w

HSC DR2, grizy

Combined scarlet model

pixels

wavelength

pixels

pixels

Combining surveys at different resolutions

HST cosmos, F814w

HSC DR2, grizy

$$Y_1$$:

$$Y_2$$:

pixels

Building a model for multi-band multi-resolution observations

A model for: multiband, SCARLET:

$$Y = AX$$

Images

SEDs

Model

What model for multi-resolution?

Shannon-Whittaker interpolation:

$$f(t_m) = \sum_{t_k}f(t_k)sinc(\frac{t_m-t_k}{h})$$

# (            )

$$f$$

$$f(t_k)$$

$$f(t_m)$$

Building a model for multi-band multi-resolution observations

HST cosmos, F814w

HSC DR2, grizy

f

f*p2

f*p2($$t_m$$)

f

f*p1

f*p1($$t_k$$)

Building a model for multi-band multi-resolution observations

Choice: high resolution frame for the model (psf & pixel size)

f

f*p2

f*p2($$t_m$$)

f

f*p1

f*p1($$t_m$$)

$$(f*p2)(t_m) = h\sum_{t_k}m(t_k)\sum_{t_l}P(t_l)sinc(\frac{t_m-t_k-t_l}{h})$$

$$(f*p_1)(t_k) = m(t_k)$$

$$\hat{P}(\nu_l) = \frac{p2}{p1}(\nu_l)$$

How does it actually look like?

HST cosmos, F814w

HSC DR2, grizy

Combined scarlet model

## Highlights

• Provides high resolution multi-band images
• Improved morphological constraints
• How do we quantify the gain?
• Ideas for scientific applications?

Combined scarlet model

## Speeding things up in 2D

$$(f*p)(x_{mx},y_{my}) = h^2 \sum_{x_{kx},x_{ky}} f(x_{kx}, y_{ky})\sum_{x_{lx}, y_{ly}}p(x_{lx},y_{ly})sinc(\frac{x_{mx}-x_{kx}-x_{lx}}{h})sinc(\frac{y_{my}-y_{ky}-x_{ly}}{h})$$

$$I_2(x_{i2},y_{j2}) = h^2 \sum_{y_{j1}} \sum_{x_{k1}}\sum_{x_{i1}} F(x_{i1}, y_{j1}) sinc(\frac{x_{i2}-x_{i1}-x_{k1}}{h} )\sum_{y_{l1}} P_d(x_{k1}, y_{l1})sinc(\frac{y_{j2}-y_{j1}-y_{l1}}{h})$$

## Making sure we are consistent

$$(rect_{h_1}*(f*p_1) *{F}^{-1}(\frac{\hat{rect_{h_2}}}{\hat{rect_{h_1}}}\frac{\hat{p_2}}{\hat{p_1}}))(x_{i2},y_{j2})= (rect_{h_2}*p_2*f)(x_{i2},y_{j2}) = I_2(x_{i2},y_{j2}).$$

By herjy

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