imgOrig=ImageResize[#,{200,200}]&@Import["https://i.pinimg.com/originals/20/3f/6e/203f6e9ce90b240ec0d18d74aba1e333.jpg"]

data=ImageData[ColorConvert[imgOrig,"Grayscale"],"Byte"];
out=Table[0,{i,1,ImageDimensions[imgOrig][[2]]},{j,1,ImageDimensions[imgOrig][[1]]}];

distort[x_]:=Round[(Norm[x]-((Norm[x])^3)*0.749)/Norm[x],1]
For[i=1,i<=ImageDimensions[imgOrig][[2]],i++,For[j=1,j<=ImageDimensions[imgOrig][[1]],j++,
out[[distort[{i,j}]*i,distort[{i,j}]*j]]=data[[i,j]]
]]

Image[out,"Byte"]

imgDist=ImageForwardTransformation[imgOrig,(#-0.5)(1+-0.6Norm[#-0.5])+0.5&]