data = Abs[ExampleData[{"TestImage", "Clock"}, "GrayLevels"] - 1];
data2 = data[[64 ;; 191, 128 ;; 255]];
pos = Position[data2, _?(# > 0.4 &)];
sample = RandomSample[pos];
h = Round[10*((data2[[#[[1]], #[[2]] ]] & /@ sample) - 0.4)/Max[data2 - 0.4]];
size = Dimensions[data2][[1]];
kernel = RotateRight[PadRight[GaussianMatrix[{15, 5}], {size, size}], {-15, -15}];
cd = RotateRight[InverseFourier[Fourier[data2]*Conjugate[Fourier[kernel]]], {10, 10}];
p0 = Table[
   GraphicsRow[{
     ArrayPlot[cd, PlotLabel -> "Diffraction limited image", LabelStyle -> {Black, Bold}],
     ArrayPlot[RotateRight[kernel, {-sample[[n, 1]] + 128, sample[[n, 2]]} ], DataReversed -> True, PlotLabel -> "Image of blinking fluorophores", LabelStyle -> {Black, Bold}],
     Graphics[{Black, PointSize[0.01], Table[{Opacity[h[[j]]/10], Point[{sample[[j, 2]], -sample[[j, 1]] + 128} ]}, {j, 1, n}]},
PlotRange -> {{0, 128}, {0, 128}}, Frame -> True, FrameTicks -> None, PlotLabel -> "Reconstructed image", LabelStyle -> {Black, Bold}]}, ImageSize -> 1000]
   , {n, 1, 5000, 10}];
ListAnimate[p0]

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This file, which was originally posted to https://twitter.com/j_bertolotti/status/1239490363968163840, was reviewed on 6 July 2020 by reviewer GRuban, who confirmed that it was available there under the stated license on that date.