Image reconstruction

Radially acquired diffusion-weighted images (DWIs) are reconstructed using the following steps:

1. Apply zero-order phase correction to each radial spoke using the average phase offset at the center slice of the lowest b-value image
2. Zerofill k-space by a factor of 2 to double field of view
3. Multiply signal of each point by its respective area on a Voronoi diagram of the points (including added zerofill points) in k-space
4. Re-grid each radially defined point to its nearest Cartesian coordinate using its Kaiser-Besel index
5. Apply Fourier transform to now Cartesian-defined k-space

This process can be easily done using the DWI Processing resources [link] link].

To use this, place both DWI_shell.ipynb and DWI_processing_functions.py in the same directory (your working directory). The readme.txt file outlines specific file formats, function inputs, and outputs.

Quickly, once all files are formatted according to readme.txt , the first cell defines all image and reconstruction parameters:

############## Parameters to change #####################
input_file = 'fid'  # k-space data
# Acquisition data
xres_ro = 128  # total readout points stored
views = 403  # number of radial views
# angl = (math.sqrt(5)-1)/2 * PI # golden angle in radians
angl = 2*PI/views  # used by Steve Pickup
# Image data
xres = 96  # actual number of points collected
yres = 96
slices = 16
bvalues = 5
b_array = np.array([10,535,1070,1479,2141])  # b-values

Each cell should then be run consecutively.