uic=ColorConvert[,"Grayscale"]

uicdata=ImageData[uic,Byte]

uicdata[[1]]

(*make sure we still have image*)

startpic=ListDensityPlot[uicdata,ColorFunction->GrayLevel,InterpolationOrder->0]

(*consider as 2D-function*)

ListPlot3D[uicdata[[1;;-1;;10]]]

(*****)
(*****)

uicf=Fourier[uicdata]

uicf[[1]]

ListDensityPlot[Map[Abs,uicf,{2}],ColorFunction->GrayLevel]

(*****)
(*****)

Length[Flatten[uicf]]

{Min[Abs@Flatten[uicf]],Max[Abs@Flatten[uicf]]}

Length[Cases[Abs@Flatten[uicf],_?(# <1 &)]]

check[x_]:=If[Abs[x]≤1,0,x];

uicnew=InverseFourier[Map[check,uicf,{2}]];

endpic=ListDensityPlot[Reverse[Map[Abs,uicnew,{2}]],ColorFunction->GrayLevel,InterpolationOrder->0]

{Show[startpic,ImageSize->500],Show[endpic,ImageSize->500]}