Sparse-Representation-Based Direct Minimum L (p)-Norm Algorithm for MRI Phase Unwrapping

A sparse-representation-based direct minimum L (p)-norm algorithm is proposed for a two-dimensional MRI phase unwrapping. First, the algorithm converts the weighted-L (p)-norm-minimization-based phase unwrapping problem into a linear system problem whose system (coefficient) matrix is a large, symmetric one. Then, the coefficient-matrix is represented in the sparse structure. Finally, standard direct solvers are employed to solve this linear system. Several wrapped phase datasets, including simulated and MR data, were used to evaluate this algorithm's performance. The results demonstrated that the proposed algorithm for unwrapping MRI phase data is reliable and robust.