The PICS tool performs iterative parallel imaging reconstruction based on a
least-squares data fidelity similar to Pruessmann et al. (2021) in a
variational formulation which optionally includes quadratic or advanced
non-quadratic regularization terms similar to Block et al. (2007).

It returns the coil-combined images in image domain.  The forward model is
scaled so that for fully sampled data and with coil sensitivities that are set
to constant one and with no regularization, a pics reconstruction corresponds
to an inverse unitary DFT.  An l1-/l2-regularization with a regularization
parameter of one is equally scaled to the data fidelty term.

For Cartesian imaging, 3D k-space (kz along z dim) must be provided.  By
default, pics assumes a 3D reconstruction (or 2D if the dimension has size one).
For a slice-by-slice 2D reconstruction, pics can be called in a loop.  If no
scaling factor is provided, pics will scale the data prior to reconstruction.
The scaling factor is calculated using the center k-space region.  This scaling
will be undone before returning if the -S flag is provided which may be
important for computing quantitative parameters.  Additional dimensions such as
coils, maps, and time must follow the dimension order specified in mri.h,
otherwise regularizers may be applied on the wrong dimensions and the forward
sense operator may be inaccurate.  If not provided, the sampling mask is determined
automatically from the provided k-space. For the sampling mask to be calculated
correctly, missing samples must be exactly zero.  Small values in k-space,
perhaps from numerical errors, will cause the sampling mask (reflected in
logged acceleration factor), and the data consistency step to be incorrect.

