Exploring the Upsampling of the BWH Diffusion Data
Extracting one a slice for one of the gradient directions of the diffusion data results in an image like this:
A two-dimensional Fourier transform leads the following magnitude images (uncentered and centered):
Representing this in the log-domain results in
Unfortunately, we don't see nice blue regions that we would have expected from ideal zero-padding. Instead it looks a little "salt-and-peppery." Is this a scanner discretization effect?
Cutting away everything that should ideally be zero gives this Fourier log-image:
An inverse Fourier transform followed by discretization results in:
The result is slighly smoother than the original, which is sensible since we essentially low-pass filtered the result.
The difference between original and reconstruction is not great, but still shows a little bit of structure: