  Purpose: To develop a general phase regularized image reconstruction method,
with applications to partial Fourier imaging, water-fat imaging and flow
imaging.
  Theory and Methods: The problem of enforcing phase constraints in
reconstruction was studied under a regularized inverse problem framework. A
general phase regularized reconstruction algorithm was proposed to enable
various joint reconstruction of partial Fourier imaging, water-fat imaging and
flow imaging, along with parallel imaging (PI) and compressed sensing (CS).
Since phase regularized reconstruction is inherently non-convex and sensitive
to phase wraps in the initial solution, a reconstruction technique, named phase
cycling, was proposed to render the overall algorithm invariant to phase wraps.
The proposed method was applied to retrospectively under-sampled in vivo
datasets and compared with state of the art reconstruction methods.
  Results: Phase cycling reconstructions showed reduction of artifacts compared
to reconstructions with- out phase cycling and achieved similar performances as
state of the art results in partial Fourier, water-fat and divergence-free
regularized flow reconstruction. Joint reconstruction of partial Fourier +
water-fat imaging + PI + CS, and partial Fourier + divergence-free regularized
flow imaging + PI + CS were demonstrated.
  Conclusion: The proposed phase cycling reconstruction provides an alternative
way to perform phase regularized reconstruction, without the need to perform
phase unwrapping. It is robust to the choice of initial solutions and
encourages the joint reconstruction of phase imaging applications.
