Model-Free Characterization of SAR MTI Time Series

Alberto Refice,Guido Pasquariello,Fabio Bovenga

doi:10.1109/lgrs.2020.3031655

Abstract

Multitemporal interferometric synthetic aperture radar (MTI) displacement time series are usually characterized by the model-dependent temporal phase coherence as a quality measure. Additional tests have to be performed to recognize other “interesting” but nonmodeled trends, and several automated approaches to this task have been proposed to date. We introduce here the fuzzy entropy ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$F_{E}$ </tex-math></inline-formula> ), a measure introduced in medical data analysis, as a viable parameter to characterize MTI time series. Being a measure of disorder in a time series, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$F_{E}$ </tex-math></inline-formula> exhibits homogeneously low values for a large class of displacement models, such as seasonal, parabolic, or piecewise linear signals, while increasing for more chaotic trends, dominated by noise. It appears therefore suited as a discriminative parameter to isolate meaningful MTI time series within large data sets, without specifying a predefined model. The calculation of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$F_{E}$ </tex-math></inline-formula> has low computational cost and can thus be easily performed as a prescreening filter. In this letter, results over simulated data and some examples on a real data set are shown with interesting performances which hint to possible large-scale implementations.

Highlights

M ULTI-TEMPORAL interferometric synthetic aperture radar (MTInSAR or Multitemporal interferometric synthetic aperture radar (MTI)) is a collection of techniques to process stacks of radar interferograms acquired over the same area with very similar geometry [1], [2]
We propose here the use of a simple feature, called Fuzzy Entropy, to characterize MTI time series
Several works have investigated the optimum values of the parameter m and r, which are common to all the various definitions of approximate, sample and fuzzy entropy, e.g., [21], [22], and the general consensus points to m = 2 and r = 0.15 × σ, where σ is the sample standard deviation of the time series, which are considered valid for a large number of signal types and applications

Summary

INTRODUCTION

M ULTI-TEMPORAL interferometric synthetic aperture radar (MTInSAR or MTI) is a collection of techniques to process stacks of radar interferograms acquired over the same area with very similar geometry [1], [2]. Most MTI detection algorithms work by maximizing the temporal coherence, so the choice of the temporal model phase trend is doubly important. The temporal coherence figure is not an exhaustive parameter to ascertain the presence of useful information in a given time series, as one may be interested in discovering temporal trends which do not follow any predefined model. This is especially true in cases when PS time series are produced independently and subsequently passed to application specialists, with the task of extracting useful information about the territory. We introduce some terminology and definition, and we test the application on both simulated and real MTI data

TIME-SERIES ENTROPY DEFINITIONS AND PROPERTIES

FUZZY ENTROPY FOR MTI TIME SERIES CHARACTERIZATION

APPLICATION TO REAL DATA

Findings

CONCLUSION