A Modified Phase Cycling Method for Complex-Valued MRI Reconstruction

Pseudocode 1

Inputs: the system matrix A,

   the measurements y,

   the maximum number of iterations K,

   the positive regularization parameter γ.

Outputs: reconstructed magnitude m and phase p.

Initialization: set the iteration index k =0,

      set the initial magnitude ,

      set the initial phase ,

      generate the set of phase wraps ω from the initial phase p₀.

Repeat: For k =1,2, …, K.

    calculate mg.

    do one-dimensional TV regularization of magnitude

    update the magnitude

    randomly choose a phase wrap w_k from ω,

    update the phase