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Use a deconvolutional neural network. There are ways to build a deconvolutional neural network that takes a source image, and then uses the neural network to build a higher-resolution version of that image. This is basically the reverse of using a convolutional neural network to simplify images into their low-resolution features. Depending on what your data ...


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Since you are on a uniform $x-y-z$ grid, you are in luck that others have had similar issues before. Specifically, I would suggest that you take a look at HDF5 for a low-level way of storing this kind of data as arrays. But in the end, you want to not just store an array, but actually do something with it: interpolate. For this, a higher-level approach would ...


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