利用L~∞+L^1范数的多基线相位解缠绕方法

L~∞+L^1-norm Method for Multi-baseline Phase Unwrapping

多基线相位解缠绕问题可以转化为求解L1范数优化问题的最优解,然而L1范数多基线相位解缠绕算法存在内存需求量大的问题,且对噪声严重的干涉相位图处理效果不理想。为了减少用线性规划算法解L1范数多基线相位解缠绕时内存需求较大的问题,该文提出用L∞范数的惩罚函数来近似L1范数的惩罚函数以减少优化模型中优化变量的大小,从而将多基线相位解缠绕模型其目标函数变为L∞范数+L1范数的形式,并且优化变量的大小减少了约57%。最后,通过一个噪声严重的实测数据对该文算法进行了验证,实验结果表明,该文提出的方法不仅可以有效地解缠绕质量较好的条纹图,同时对噪声严重区还具有一定的滤波效果。

Multi-baseline phase unwrapping problem can be solved according to find the optimal solution of the L1-norm optimization. However, there are two problems： one is the huge memory required and the other is the difficulty in processing interferograms with severe noise. In order to decrease the memory requirement of the L1-norm method, with a cost function of L∞-norm is employed to approximate the L1-norm. Consequently, the objective function of the improved multi-baseline phase unwrapping is the form of L∞-norm＋L1-norm, and the size of the new optimization variable is decreased by 57%. The performance of the proposed algorithm is validated via a real dataset with severe noise present, and the experiment demonstrates that the proposed algorithm not only presents a well phase unwrapping result of interferograms with good quality, but also performs a filtering against noise region.