Time Series Phase Unwrapping Algorithm Using LP-norm Optimization Compressive Sensing

Time series phase unwrapping is an essential step in the time series interferometric synthetic aperture radar technique for deformation monitoring. However, traditional unwrapping algorithms are prone to unwrapping errors in the case of intense noise and steep deformation gradients, which directly affect the accuracy of the deformation information interpretation. To address this problem, a time series phase unwrapping algorithm using LP-norm optimization compressive sensing is proposed in this paper. This algorithm first transforms the minimizing L0-norm describing compressive sensing technique into a nonconvex problem with weaker constraints, that is, minimizing the LP-norm. Then, an optimized compressed sensing model was proposed by combining the constraint criterion of the phase triplet closure in the temporal domain and the solution strategy of the iterative reweighted least squares method. Improved temporal dimensional phase unwrapping and unwrapping error correction algorithms were developed based on this optimized model. Finally, the proposed algorithm was perfected by combining the above improved methods and the pseudo-three-dimensional phase unwrapping framework. Simulated and Sentinel-1A real datasets verify that the proposed algorithm has better noise robustness, unwrapping stability, and efficiency than traditional algorithms, particularly in the case of a steep deformation gradient and intense noise. The temporal coherence estimated by the proposed algorithm for the real dataset is generally greater than 0.99, which is far superior to traditional algorithms. Furthermore, the proposed algorithm facilitates high-precision interpretation of deformation information. The cross-validation results show that the deformation results obtained by traditional algorithms are underestimated by at least 73 mm/a and 68 mm at the maximum subsidence than the DSInSAR. However, the deformation result obtained by the proposed algorithm is highly consistent with that of the DSInSAR.