A Novel Mixed-Norm Multibaseline Phase-Unwrapping Algorithm Based on Linear Programming

The multibaseline phase unwrapping (PU) of L
¹
-norm can be efficiently solved using linear programming. However, the huge memory requirement of linear programming limits its application in multibaseline PU for large-scale data. In order to reduce the required memory when linear programming is performed, a novel mixed-norm multibaseline PU algorithm is proposed in this letter, which is regarded as an approximation of the L
¹
-norm method. In this method, an L∞-norm cost function is employed to substitute for that of the L
¹
-norm, i.e., it takes the optimization which is aimed to minimize the maximum component of the optimization variable as the representation of the one that minimizes the absolute sum of L
¹
-norm. Consequently, the cost function in the proposed method changes to be an L
¹
-norm plus an L
^∞
-norm. Compared with the traditional L
¹
-norm method, the size of the optimization variable in the proposed method is generally reduced by about one-seventh. Therefore, it is logical that less memory is needed in the proposed algorithm. The effectiveness of the proposed algorithm is validated via a simulated and real repeat-pass interferometric-synthetic-aperture-radar data set.