Persistent scatterer interferometry (PSI) techniques exploit irregularly spaced permanent scatters (PSs) to extract the ground deformation. Sparse 2-D phase unwrapping is a significant procedure in PSI methods to reconstruct the phase function defined on a sparse data set given its value modulo 2λ . This letter first analyzes the phase unwrapping error of the residues and cuts related local methods when the cuts separate the sparse grids into several isolated regions. Then the space distribution of the cuts is converted into constraints on optimizing the Delaunay triangulation network. Finally, the phase jumps introduced by PSs with low quality are removed due to the more reasonable flows obtained by the constrained L <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> -norm method. Two experiments performed on the real data sets are presented to show the effectiveness and robustness of our algorithm, especially in the long-span cable-stayed bridge applications.