File:Deconvolution with imperfect kernels.png
Summary
| Description |
English: If you know the response function of your instrument, you can deconvolve it from your measurement to obtain a much sharper signal. But deconvolution is a dangerous procedure, as small mistakes in the kernel can result in heavy artifacts. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1126058724722917377 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 11.0 code
data = Abs[ExampleData[{"TestImage", "Tree"}, "GrayLevels"] - 1];
size = Dimensions[data][[1]];
kernel = RotateRight[
PadRight[GaussianMatrix[30], {size, size}], {-30, -30}];
cd = InverseFourier[Fourier[data]*Conjugate[Fourier[kernel]]];
ikernel = kernel; ikernel[[20, 20]] = Max[kernel];
nkernel =
RotateRight[
PadRight[
GaussianMatrix[30]*RandomReal[{0.5, 1.5}, {61, 61}], {size, size}], {-30, -30}];
p1 = Grid[{{ ArrayPlot[cd, Frame -> False], "deconvolved\n with", ArrayPlot[RotateRight[kernel, {size/2, size/2}] , PlotLabel -> "Perfect kernel"], "\[Rule]", ArrayPlot[InverseFourier[Fourier[cd]/Conjugate[Fourier[kernel]]], Frame -> False]},
{ ArrayPlot[cd, Frame -> False], "deconvolved\n with", ArrayPlot[RotateRight[ikernel, {size/2, size/2}] , PlotLabel -> "Imperfect kernel\n(one pixel wrong)"], "\[Rule]",
ArrayPlot[InverseFourier[Fourier[cd]/Conjugate[Fourier[ikernel]]], Frame -> False]},
{ ArrayPlot[cd, Frame -> False], "deconvolved\n with", ArrayPlot[RotateRight[nkernel, {size/2, size/2}],
PlotLabel -> "Imperfect kernel\n(noisy)" ], "\[Rule]", ArrayPlot[InverseFourier[Fourier[cd]/Conjugate[Fourier[nkernel]]], Frame -> False]}
}, Alignment -> {Center, Center, {{1, 1} -> Bottom, {2, 1} -> Bottom, {3, 1} -> Bottom, {1, 5} -> Bottom, {2, 5} -> Bottom, , {3, 5} -> Bottom}}]
Licensing
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