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

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 L1-norm is more robust than L2-norm cost function minimization if the data set has a large number of outlying points. In this paper, we present an L1-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 L2-norm solutions.

[1]  F. Casu,et al.  An Overview of the Small BAseline Subset Algorithm: a DInSAR Technique for Surface Deformation Analysis , 2007 .

[2]  Peter J. Huber,et al.  Robust Statistics , 2005, Wiley Series in Probability and Statistics.

[3]  Riccardo Lanari,et al.  Satellite radar interferometry time series analysis of surface deformation for Los Angeles, California , 2004 .

[4]  H. Zebker,et al.  Persistent scatterer interferometric synthetic aperture radar for crustal deformation analysis, with application to Volcán Alcedo, Galápagos , 2007 .

[5]  R. Yarlagadda,et al.  Fast Algorithms for lp Deconvolution , 1985 .

[6]  J. Scales,et al.  Robust methods in inverse theory , 1988 .

[7]  Antonio Pepe,et al.  On the Extension of the Minimum Cost Flow Algorithm for Phase Unwrapping of Multitemporal Differential SAR Interferograms , 2006, IEEE Transactions on Geoscience and Remote Sensing.

[8]  A. Gersztenkorn,et al.  Robust iterative inversion for the one‐dimensional acoustic wave equation , 1986 .

[9]  D. Schmidt.  Time-dependent land uplift and subsidence in the Santa Clara Valley , 2003 .

[10]  Fabio Rocca,et al.  Nonlinear subsidence rate estimation using permanent scatterers in differential SAR interferometry , 2000, IEEE Trans. Geosci. Remote. Sens..

[11]  J. Tukey,et al.  The Fitting of Power Series, Meaning Polynomials, Illustrated on Band-Spectroscopic Data , 1974 .

[12]  George E. Hilley,et al.  Resolving vertical tectonics in the San Francisco Bay Area from permanent scatterer InSAR and GPS analysis , 2006 .

[13]  Gianfranco Fornaro,et al.  A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms , 2002, IEEE Trans. Geosci. Remote. Sens..

[14]  P. Rosen,et al.  Atmospheric effects in interferometric synthetic aperture radar surface deformation and topographic maps , 1997 .

[15]  Riccardo Lanari,et al.  A quantitative assessment of the SBAS algorithm performance for surface deformation retrieval from DInSAR data , 2006 .

[16]  D. O’Leary.  Robust regression computation computation using iteratively reweighted least squares , 1990 .

[17]  C. W. Chen,et al.  Two-dimensional phase unwrapping with use of statistical models for cost functions in nonlinear optimization. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[18]  Yngvar Larsen,et al.  Detailed rockslide mapping in northern Norway with small baseline and persistent scatterer interferometric SAR time series methods. , 2010 .

[19]  R. Bürgmann,et al.  Earthquake potential along the northern hayward fault, california , 2000, Science.

[20]  Mario Costantini,et al.  A novel phase unwrapping method based on network programming , 1998, IEEE Trans. Geosci. Remote. Sens..

[21]  J. Claerbout,et al.  Robust Modeling With Erratic Data , 1973 .

[22]  Yngvar Larsen,et al.  A generic differential interferometric SAR processing system, with applications to land subsidence and snow-water equivalent retrieval , 2006 .

[23]  J. Bee Bednar,et al.  Fast algorithms for lpdeconvolution , 1985, IEEE Trans. Acoust. Speech Signal Process..

[24]  C. Werner,et al.  Satellite radar interferometry: Two-dimensional phase unwrapping , 1988 .

[25]  Howard A. Zebker,et al.  Decorrelation in interferometric radar echoes , 1992, IEEE Trans. Geosci. Remote. Sens..

[26]  Ramon F. Hanssen,et al.  Interferometric phase analysis for monitoring slow deformation processes , 1997 .

[27]  Fabio Rocca,et al.  Modeling Interferogram Stacks , 2007, IEEE Transactions on Geoscience and Remote Sensing.

[28]  E. Schlossmacher.  An Iterative Technique for Absolute Deviations Curve Fitting , 1973 .

[29]  Fabio Rocca,et al.  Permanent scatterers in SAR interferometry , 1999, Remote Sensing.

[30]  Riccardo Lanari,et al.  Application of the SBAS-DInSAR technique to fault creep: A case study of the Hayward fault, California , 2007 .

[31]  M. Costantini,et al.  A generalized phase unwrapping approach for sparse data , 1999, IEEE 1999 International Geoscience and Remote Sensing Symposium. IGARSS'99 (Cat. No.99CH36293).

[32]  Gianfranco Fornaro,et al.  LMMSE 3-D SAR Focusing , 2009, IEEE Transactions on Geoscience and Remote Sensing.

[33]  R. Goldstein,et al.  Mapping small elevation changes over large areas: Differential radar interferometry , 1989 .

[34]  R. Hanssen.  Radar Interferometry: Data Interpretation and Error Analysis , 2001 .

[35]  Robert M. Nadeau,et al.  Distribution of aseismic slip rate on the Hayward fault inferred from seismic and geodetic data , 2005 .

[36]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[37]  Andrew Hooper,et al.  A multi‐temporal InSAR method incorporating both persistent scatterer and small baseline approaches , 2008 .

[38]  Fuk K. Li,et al.  Synthetic aperture radar interferometry , 2000, Proceedings of the IEEE.