Adapt the following functions for color image processing using separate processing of RGB channels and processing of an extracted Y $($luma$-$

luminosity$)$ channel from the YUV space with the further recreation of an RGB image $($you may design your own functions for RGB$-$YUV and YUV$-$RGB transformations or use Matlab functions rgb$2$ycbcr and ycbcr$2$rgb$,$ to extract a Y channel and re$-$create and RGB image, respectively$)$:

a$)$ a function utilizing a smart linear filter $(1/16*[1,2,1$; $2,4,2$; $1,2,1])$

b$)$ A function utilizing median filter

$2.$ In the Pepper$\_$Gaussian.tif image, all its three color channels are corrupted by an additive Gaussian noise with a different standard deviation. Filter this image using a smart filter applied to each of RGB channels separately and only to the Y $($luma$-$luminosity$)$ channel. Compare the results of filtering to the original image Pepper.tif in terms of PSNR$/$RSME measured separately for each of the color channels and the Y channel. Show the code.

$3.$ In the Pepper$\_$Impulse.tif image, all its three color channels are corrupted by an impulse noise with slightly different corruption rates of $0\mathrm{.}0070\mathrm{.}012.$ Filter this image using a median filter applied to each of RGB channels separately and only to the Y $($luma$-$luminosity$)$ channel. Compare the results of filtering to the original image Pepper.tif in terms of PSNR$/$RSME measured separately for each of the color channels and the Y channel. Show the code.