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I do Fourier Transform for an image, then consider line(slice) in FFT image. When that slice isn't parallel neither x- not y-axis, coordinates are not integer. E.g. slice can hold indices {(0,0), (0.25,1), (0.5,2), (0.75,3), (1,4)...}. When using nearest-interpolation, quality of whatever I do is pure.

What techniques can you suggest to improve interpolation in Fourier grid?

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  • $\begingroup$ Welcome to DSP.SE! I'm not sure what you mean by "When using nearest-interpolation, quality of whatever I do is pure." Could you rephrase it? $\endgroup$ – Peter K.♦ Sep 25 '15 at 16:26
  • $\begingroup$ @Peter K. : I want to calculate invertible Radon transform using Projection-Slice theorem. So, when for point (0.75, 3) use value at (1,3), and then perform inverse transform, reconstruction is not perfect. $\endgroup$ – Olha Pavliuk Sep 25 '15 at 16:33
  • $\begingroup$ Are all your coordinates multiples of 0.25 or such? $\endgroup$ – Olli Niemitalo Sep 26 '15 at 7:19
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The usual way to do this is to interpolate using surrounding points. There is a simple 6-point mechanism that uses:

enter image description here

This question on the Mathematics SE site has some more details. Note the answer's correction to the equation in the question.

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