MRI using receiver arrays with many coil elements can provide high signal-to-noise ratio and increase parallel imaging acceleration. At the same time, the growing number of elements results in larger datasets and more computation in the reconstruction. This is of particular concern in 3D acquisitions and in iterative reconstructions. Coil compression is effective in mitigating this problem by compressing data from many channels into fewer virtual coils. Among different coil compression methods, data-based coil compression is most effective and does not rely on the explicit knowledge of the coil sensitivities.
In Cartesian sampling there often are fully sampled k-space dimensions. A spatially varying coil compression can therefore be exploited in these fully sampled directions to further reduce the number of virtual coils. A geometric-decomposition coil compression (GCC) is proposed here that includes different coil compressions at individual spatial locations and an alignment of coil compression matrices. The alignment guarantees the smoothness of the virtual coil sensitivites and provides compatibility with autocalibrating parallel imaging reconstructions.
More details of the coil compression algorithm can be found in the references. I have provided a MATLAB example of the algorithm.
A complete MATLAB-based coil compression package can be downloaded here. It is much slower than the OMP,C++ version. The C++ version will be released soon.