InSAR Deformation Time Series Using an $L_{1}$-Norm Small-Baseline Approach

Abstract

Satellite synthetic aperture radar interferometry (InSAR) is an invaluable tool for land displacement monitoring. Improved access to time series of satellite data has led to the development of several innovative multitemporal algorithms. Small baseline (SB) is one such time-series InSAR method, based on combining and inverting a set of unwrapped interferograms for surface displacement. Two-dimensional unwrapping of sparse data sets is a challenging task, and unwrapping errors can lead to incorrectly estimated deformation time series. It is well known that L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm is more robust than L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm cost function minimization if the data set has a large number of outlying points. In this paper, we present an L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm-based SB method using an iteratively reweighted least squares algorithm. We show that the displacement phase of both synthetic data, as well as a real data set that covers the San Francisco Bay area, is recovered more accurately than with L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm solutions.