Updating a DInSAR time series using a modified SBAS algorithm with an incremental SVD: Preliminary results

RAYNER DE RUYT; EUILLADES, PABLO A.; EUILLADES, LEONARDO; CASELLI, ALBERTO

Helsinki

Workshop; Fringe 2017 Workshop; 2017

European Space Agency

One  limitation  of  the  algorithms  for  computing  DInSAR  time  series  is  that  all  available  data  must  be  processed  at  once.  So,  in  order  to  update  the  time  series  the  whole  dataset  must  be  reprocessed  when  new  scenes  arrive.  Considering the growing number of available acquisitions and the shortening of revisit time between them, this affects the potential of this type of techniques to be transformed into semi-real time monitoring systems[1]. One of the most used  algorithms  for  computing  deformation  time-series  is  Small  Baseline  Subset  (SBAS).  It  estimates  the  temporal  evolution of surface displacement based on SAR images pairs characterized by low temporal and geometric baselines [2]. The algorithm?s core is to invert the relative displacement between SAR scenes using a minimum norm criteria, and implemented via the Singular Value Decomposition (SVD).In this contribution we propose a modification to the SBAS algorithm which allows recursively adding new scenes to an already computed time-series. Given a time-series obtained from a number of already acquired scenes ia the SVD-based  inversion,  including  and  additional  acquisition  is  performed  with  the  following  steps:  1)  computing  new  differential interferograms between the new scene and a number of old ones, taking care of not exceed the temporal and  geometric  baseline  limitations,  2)  update  the  coherence  masks  by  considering  the  new  interferograms,  3)  independently unwrap the new interferograms by using the updated coherence mask [3] and 4) re-compute the time-series by using a modification low-rank algorithm for a thin SVD [4] The  last  step consist  in  updating  the  thin  SVD  of  the  incidence-like  matrix  generated  in  the  original  processing.  In  particular,  we  modify  its  eigenvalues,  and  subsequently  their  respective  left  and  right  singular  vectors,  through  the  virtual insertion of rows (interferograms) and columns (SAR images) in the aforementioned matrix. This way we are able of updating the equation system solution without re-computing the whole inversion.We  applied  the  proposed  algorithm  to  114  COSMO-Skymed  stripmap  scenes  acquired  between  June  2011  and  July  2013 at the Caviahue Copahue Volcanic Complex (border between Argentina and Chile). The CCVC has suffered recent eruptive  activity,  showing  an  inflation  process  of  approximately  7  cm/year  centered  in  the  northern  flank  of  the  Copahue  Volcano  [5].  Temporal  and  perpendicular  baseline  constrains  are  365  days  and  600  meters,  respectively.  ASTER  GDEM  was  employed  for  topographic  phase  compensation.  Phase  unwrapping  was  performed  using  the  Minimum Cost Flow algorithm. Firstly,  we  computed  a  time  series  via  SBAS  processing  of  the  whole  dataset,  in  order  to  generate  a  known  result.  Then, we constructed a partial solution by using the first 52 scenes and subsequently increased the number of scenes by executing steps 1 to 4 mentioned previously. Preliminary comparative results indicate that the time-series obtained by updating the solution shows high correlation with the control results. The comparison was performed over pixels present at the updated coherence mask, within and outside the deformation area.Future  development  will  focus  in  testing  different  case  studies,  particularly  a  synthetic  one,  and  incorporating  algorithms which allow increasing the optimization and numeric stability of the results.  References[1]        P.  S.  Marinkovic,  F.  van  Leijen,  G.  Ketelaar,  and  R.  F.  Hanssen,  ?Recursive  data  processing  and  data  volume  minimization  for  PS-InSAR,?  in  Proceedings.  2005  IEEE  International  Geoscience  and  Remote  Sensing  Symposium,  2005. IGARSS ?05., 2005, vol. 4, pp. 2697?2700.[2]    P. Berardino, G. Fornaro, R. Lanari, and E. Sansosti, ?A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms,? IEEE Trans. Geosci. Remote Sens., vol. 40, no. 11, pp. 2375?2383, Nov. 2002.[3]    M. Costantini, ?A novel phase unwrapping method based on network programming,? IEEE Trans. Geosci. Remote Sens., vol. 36, no. 3, pp. 813?821, May 1998.[4]    M. Brand, ?Fast low-rank modifications of the thin singular value decomposition,? Linear Algebra Its Appl., vol. 415, no. 1, pp. 20?30, May 2006.[5]        Copahue  Volcano,  F.  Tassi,  O.  Vaselli,  A.T.  Caselli,  Editors,  Active  Volcanoes  of  the  World  Series,  Ed.  Springer-Verlag, Berlin Heidelberg, 2016