Rémy Joseph, Peter Melchior,
Fred Moolekamp
Spoiler Alert!
HST cosmos, F814w
HSC DR2, grizy
Combined scarlet model
pixels
wavelength
Combining surveys at different resolutions
\(Y_1\):
\(Y_2\):
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:
\(f(t_m) = \sum_{t_k}f(t_k)sinc(\frac{t_m-t_k}{h})\)
\(f\)
\(f(t_k)\)
\(f(t_m)\)
f
f*p2
f*p2(\(t_m\))
f*p1
f*p1(\(t_k\))
Choice: high resolution frame for the model (psf & pixel size)
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?
\( (f*p)(x_{mx},y_{my}) = h^2 \sum_{x_{kx},x_{ky}} f(x_{kx}, y_{ky})\sum_{x_{lx}, y_{ly}}p(x_{lx},y_{ly})sinc(\frac{x_{mx}-x_{kx}-x_{lx}}{h})sinc(\frac{y_{my}-y_{ky}-x_{ly}}{h})\)
\(I_2(x_{i2},y_{j2}) = h^2 \sum_{y_{j1}} \sum_{x_{k1}}\sum_{x_{i1}} F(x_{i1}, y_{j1}) sinc(\frac{x_{i2}-x_{i1}-x_{k1}}{h} )\sum_{y_{l1}} P_d(x_{k1}, y_{l1})sinc(\frac{y_{j2}-y_{j1}-y_{l1}}{h}) \)
\((rect_{h_1}*(f*p_1) *{F}^{-1}(\frac{\hat{rect_{h_2}}}{\hat{rect_{h_1}}}\frac{\hat{p_2}}{\hat{p_1}}))(x_{i2},y_{j2})= (rect_{h_2}*p_2*f)(x_{i2},y_{j2}) = I_2(x_{i2},y_{j2}).\)
By herjy