  The 2D phase unwrapping problem seeks to recover a phase image from its
observation modulo 2$\pi$, and is a crucial step in a variety of imaging
applications. In particular, it is one of the most time-consuming steps in the
interferometric synthetic aperture radar (InSAR) pipeline. In this work we
tackle the $L^1$-norm phase unwrapping problem. In optimization terms, this is
a simple sparsity-inducing problem, albeit in very large dimension. To solve
this high-dimensional problem, we iteratively solve a series of numerically
simpler weighted least squares problems, which are themselves solved using a
preconditioned conjugate gradient method. Our algorithm guarantees a sublinear
rate of convergence in function values, is simple to implement and can easily
be ported to GPUs, where it significantly outperforms state of the art phase
unwrapping methods.
