SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\ExQu"]

img=Import["figs/Taylor-8.png"]

Dimensions[im=ImageData[img]]

Table[
bs=2^(8-k);
ps = Graphics[
Raster[Reverse[Total[Partition[im, {bs,bs}], {3,4}]/bs^2.]
],
ImageSize -> 256, ImagePadding -> None, PlotRangePadding -> None
];
Export["figs/Taylor-"<>ToString[k]<>".png", ps];
ps,
{k,{3,4,5}}
]