View source for July31T-con/PlayingWithTheDiffusionData

== 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: <br>

[[Image:original.png|500px]]

A two-dimensional Fourier transform leads the following magnitude images (uncentered and centered):

[[Image:fouriermagnitude.png|500px]]
[[Image:fouriermagnitude-centered.png|500px]]

Representing this in the log-domain results in

[[Image:logfouriermagnitude.png|500px]]
[[Image:logfouriermagnitude-centered.png|500px]]

Cutting away everything that should ideally be zero gives this Fourier log-image:

[[Image:Logfouriermagnitude-centered-and-cut.png|500px]]

An inverse Fourier transform followed by discretization results in:

[[Image:reconstructed.png|500px]]

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:

[[Image:reconstruction-diffference.png|500px]]


In case you want to recreate the results. Here is the matlab script [[media:dwiTstScript.m|dwiTstScript.m]]. And here is the data [[media:SampleDWIDataSlice.tar.gz|SampleDWIDataSlice.tar.gz]].