  Combining fast MR acquisition sequences and high resolution imaging is a
major issue in dynamic imaging. Reducing the acquisition time can be achieved
by using non-Cartesian and sparse acquisitions. The reconstruction of MR images
from these measurements is generally carried out using gridding that
interpolates the missing data to obtain a dense Cartesian k-space filling. The
MR image is then reconstructed using a conventional Fast Fourier Transform. The
estimation of the missing data unavoidably introduces artifacts in the image
that remain difficult to quantify.
  A general reconstruction method is proposed to take into account these
limitations. It can be applied to any sampling trajectory in k-space, Cartesian
or not, and specifically takes into account the exact location of the measured
data, without making any interpolation of the missing data in k-space.
Information about the expected characteristics of the imaged object is
introduced to preserve the spatial resolution and improve the signal to noise
ratio in a regularization framework. The reconstructed image is obtained by
minimizing a non-quadratic convex objective function. An original rewriting of
this criterion is shown to strongly improve the reconstruction efficiency.
Results on simulated data and on a real spiral acquisition are presented and
discussed.
