MRI Partial Fourier reconstruction with POCS

Fast and robust reconstruction of Cartesian partial Fourier MRI data with POCS

POCS (Projection Onto Convex Sets) is often used to reconstruct partial Fourier MRI data.
This implementation works with 2D or 3D data on a Cartesian grid. It is optimized for speed and automatically detects the asymmetrically sampled dimension.

Input data is generally assumed to be a multi-channel k-space signal, with the first dimension for the channels (or coils). You can, however, pass a pure 2D array.

[im, kspFull] = pocs( kspIn, iter, watchProgr )

=== Input ===

kspIn: Reduced Cartesian MRI Data-Set
Any dimension may be reduced,
but only one reduction dim. is allowed due to Physics/Math.

Allowed shapes for kspIn are...
... Ny x Nx
... Nc x Ny x Nx
... Nc x Ny x Nx x Nz

With Nc == number of receive Channels / Coils.

kspIn can either be a zero-padded array, so the partial Fourier property is obvious.
Or kspIn can be the measured data only, then we try to find k-space centre automagically
and create a zero-padded array with the full size, first.
Errors are however more likely to occur in the latter case.

iter: No. of iterations
(optional) default: iter = 20
Try on your own if larger iter improves your results!

watchProgr: true/false; Whether the progress of the reconstruction should
(optional) be monitored in an image window.
In 3D data, only the central partition will be shown.

=== Output ===

im: Reconstructed Images (channels not combined)

kspFull: Reconstructed full k-space data (just the Fourier transformed im)