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MRI Partial Fourier reconstruction with POCS

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MRI Partial Fourier reconstruction with POCS

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07 Dec 2012 (Updated )

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

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Description

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)

MATLAB release MATLAB 8.0 (R2012b)
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Updates
14 Dec 2012

Smoothed transition between measured signal and reconstructed data to reduce Gibbs ringing.
Added example script

19 Dec 2012

* more loose dimension-detection
* better before/after screenshot

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