# How to upscale (reduce the spatial resolution) a satellite image using a Gaussian kernel (i.e., point spread function)?

I am trying to figure out how to upscale a satellite image using a Gaussian kernel (sigma = 0.5) from 15m to 460m spatial resolution. I am following the paper The effect of point spread function on downscaling continua where the authors at p.253 in Eq(9) they mention, and I quote,: the coarse image produced by upscaling the corresponding fine band k using a PSF. I googled how I can achieve that but unfortunately I couldn't find any solution. Could you please assist me on how can I do that in R?
Here is the image I want to upscale:

``````new("RasterLayer", file = new(".RasterFile", name = "C:\\Users\\Geography\\Desktop\\a\\pan.tif",

datanotation = "FLT4S", byteorder = "little", nodatavalue = -Inf,

NAchanged = FALSE, nbands = 1L, bandorder = "BIL", offset = 0L,

toptobottom = TRUE, blockrows = 256L, blockcols = 256L, driver = "gdal",

open = FALSE), data = new(".SingleLayerData", values = logical(0),

offset = 0, gain = 1, inmemory = FALSE, fromdisk = TRUE,

isfactor = FALSE, attributes = list(), haveminmax = FALSE,

min = Inf, max = -Inf, band = 1L, unit = "", names = "pan"),

legend = new(".RasterLegend", type = character(0), values = logical(0),

color = logical(0), names = logical(0), colortable = logical(0)),

title = character(0), extent = new("Extent", xmin = 582700,

xmax = 604300, ymin = 1005700, ymax = 1047400), rotated = FALSE,

rotation = new(".Rotation", geotrans = numeric(0), transfun = function ()

NULL), ncols = 216L, nrows = 417L, crs = new("CRS", projargs = "+proj=lcc +lat_0=18.88015774 +lon_0=76.75 +lat_1=16.625 +lat_2=21.125 +x_0=1000000 +y_0=1000000 +datum=WGS84 +units=m +no_defs"),

history = list(), z = list())
``````

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