Interpolation

Anything related to function interpolation, i.e

Splines

Smooth polynomial functions that are piecewise-defined.

Others

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I did the math for interpolation with trig functions rather than polynomials as mdurant suggested;it turns out to be very similar to the cubic splines from question 2D Interpolation with periodic boundary conditions |

Finding a local maximum of an interpolation splines is an easy enough thing;note that you should generally use a true splines from question Finding an approximate local maximas with noisy data in Matlab |

That is you could use to give but for the more interesting case of images like you mention at the end of your question then the axes probably won t be integer multiples and you ll be from question How to overplot arrays of different shape? |

I think you re using few values for the interpolation by changing to i get the following and changint the splines degree to i get the following i think a good starting point for the interpolation could be n 2 and as the interpolation from question How to smooth and plot x vs weighted average of y, weighted by x? |

With a lower order splines that works from question Why does InterpolatedUnivariateSpline return nan values |

I am quite free in terms of the type of the interpolation but it shouldn t be too fancy nothing from question Vectorized interpolation on array with nans |

Using a zero-padded ifft to upsample produces a similar high quality interpolation except for circular boundary effects;if you have to use 1 of your 3 available methods splines from question Which interpolation method to use for resampling speech signal? |