  We propose a k-space preconditioning formulation for accelerating the
convergence of iterative Magnetic Resonance Imaging (MRI) reconstructions from
non-uniformly sampled k-space data. Existing methods either use sampling
density compensations which sacrifice reconstruction accuracy, or circulant
preconditioners which increase per-iteration computation. Our approach
overcomes both shortcomings. Concretely, we show that viewing the
reconstruction problem in the dual formulation allows us to precondition in
k-space using density-compensation-like operations. Using the primal-dual
hybrid gradient method, the proposed preconditioning method does not have inner
loops and are competitive in accelerating convergence compared to existing
algorithms. We derive l2-optimized preconditioners, and demonstrate through
experiments that the proposed method converges in about ten iterations in
practice.
