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Accounting for the point spread function when downscaling a satellite image using a spectral index as covariate

Nikolaos Tziokas 
Hi, I want to downscale a nighttime lights satellite image (VIIRS DNB)
using as covariate a spectral index (Normalize Difference Vegetation
Index-NDVI) calculated from Landsat 8. For the downscaling I am using
geographically
weighted regression and area-to-point kriging. I'd like to account for
the Point
Spread Function (PSF) during downscaling. For this reason, I am following
the paper of Wang et al., (2020) '*The effect of point spread function on
downscaling continua*'. On page 254 they mention the necessary steps for
approximation of the PSF:

   1.

   *The fine spatial resolution band (e.g., 10 m Sentinel-2 band) is
   convolved with a Gaussian PSF (with scale parameter ?i) and upscaled to the
   coarse spatial resolution (e.g., 20 m).*
   2.

   *For the coarse band, a linear regression model is fitted between the
   upscaled image (e.g., 20 m Sentinel-2 image) and the observed coarse image
   (e.g., the observed 20 m Sentinel-2 image). The CC is calculated.*
   3.

   *Step (2) is conducted for all parameter candidates of ?. For the
   visited coarse band, the optimal ? is estimated as the one leading to the
   largest CC in (2).*

Their paper differs from my methodology because they used as covariate a
single spectral band (and it's PSF) to downscale one other spectral band,
while in my case I am using a spectral index (NDVI) which is a combination
of spectral bands. My question is this: how should I approach for the
approximation of the PSF of NDVI? I already downscaled the VIIRS DNB but
without taking into account the PSF. I used the atakrig package. I can
share my code but I thought it would be irrelevant in this point. Thank you.