MRI Partial Fourier reconstruction 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)