Multi-temporal InSAR (MTI) displacement time series are usually characterized by the merit figure known as temporal phase coherence, which is the vector sum on the complex residues left after removing a model phase trend, which is imposed a priori. Most MTI detection algorithms work in fact by detecting stable scatterers through maximization of the temporal coherence, so the choice of the temporal model is doubly important. Many processing chains make use of a linear model (constant velocity), while others use a wider repertoire, such as polynomial or periodic functions [1, 2]. Some MTI algorithms do not explicitly impose an a priori phase model, but nevertheless rely on some smoothness criteria in the temporal dimension to identify the stable pixels [3]. Clearly, then, the temporal coherence figure is not an exhaustive parameter to ascertain a posteriori the presence of useful information in a given MTI pixel time series, and it should be used with caution as a stable point detection criterion, as time series with low noise, following models different from the ones postulated in the detection step, will exhibit low coherence values, together with uninteresting, noisy time series. Moreover, one may be interested in discovering temporal trends which do not follow any of the predefined models used in the processing. 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. It should also be considered that MTI datasets are increasingly made available over wide areas, such as entire national [4, 5] and even continental scales, with computational loads which discourage extended use of a priori models more complex than the simplest ones. Thus, typically, additional tests have to be performed to recognize other "interesting" but non-modeled trends, and some automated approaches to this task have been proposed to date [6]. We propose here the fuzzy entropy (FuzEn), a quantity originally developed for medical time series analysis, as a viable parameter to characterize multi-temporal InSAR time series, in order to isolate smooth, or temporarily smooth trends without a predefined model. FuzEn [7] basically measures the degree of regularity of a given time series by comparing short sub-sequences of samples according to a given distance measure, typically the Chebyshev distance in the original formulation, which can be easily substituted by e.g. a distance defined on the circle to deal with possible unwrapping errors. Being a measure of disorder in a time series, FuzEn exhibits homogeneously low values for a large class of displacement models, such as seasonal, parabolic or piecewise linear signals, or series with a few discontinuities, while increasing for more chaotic trends, dominated by noise. It appears therefore suited as a model-free discriminative parameter to isolate a few meaningful MTI pixels time series within large datasets. It also exhibits good potential as an a priori criterion for stable scatterer detection. The calculation of FuzEn has low computational cost and can thus be easily performed in batch, as a pre-screening filter. In the presentation, some results over simulated data and some examples on a real dataset are shown, with interesting performances which hint to possible large-scale implementations. References [1] M. Crosetto, O. Monserrat, M. Cuevas-González, N. Devanthéry, G. Luzi, and B. Crippa, "Measuring thermal expansion using X-band persistent scatterer interferometry," ISPRS J. Photogramm. Remote. Sens., vol. 100, pp. 84-91, may 2015. [2] Y. Morishita and R. F. Hanssen, "Deformation Parameter Estimation in Low Coherence Areas Using a Multisatellite InSAR Approach," IEEE Transactions on Geosci. Remote. Sens., vol. 53, no. 8, pp. 4275-4283, 2015. [3] P. Berardino, G. Fornaro, R. Lanari, and E. Sansosti, "A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms," IEEE Transactions on Geosci. Remote. Sens., vol. 40, no. 11, pp. 2375-2383, 2002. [4] M. Caro Cuenca, R. F. Hanssen, A. J. Hooper, and M. Arikan, "Surface deformation of the whole Netherlands after PSI analysis," in FRINGE Workshop Proceedings, pp. 1-27, 2013. [5] M. Costantini, et al., "Analysis of surface deformations over the whole Italian territory by interferometric processing of ERS, Envisat and COSMO-SkyMed radar data," Remote. Sens. Environ., vol. 202, pp. 250-275, dec 2017. [6] M. Berti, A. Corsini, S. Franceschini, and J. P. Iannacone, "Automated classification of Persistent Scatterers Interferometry time series," Natural Hazards and Earth System Science, vol. 13, no. 8, pp. 1945-1958, Aug. 2013. [7] Weiting Chen, Zhizhong Wang, Hongbo Xie, and Wangxin Yu, "Characterization of Surface EMG Signal Based on Fuzzy Entropy," IEEE Transactions on Neural Syst. Rehabil. Eng., vol. 15, no. 2, pp. 266-272, 2007.
Model-Free Characterization of Low-Noise, Nonlinear MTI Time Series
Refice Alberto;Bovenga Fabio;Pasquariello Guido
2021
Abstract
Multi-temporal InSAR (MTI) displacement time series are usually characterized by the merit figure known as temporal phase coherence, which is the vector sum on the complex residues left after removing a model phase trend, which is imposed a priori. Most MTI detection algorithms work in fact by detecting stable scatterers through maximization of the temporal coherence, so the choice of the temporal model is doubly important. Many processing chains make use of a linear model (constant velocity), while others use a wider repertoire, such as polynomial or periodic functions [1, 2]. Some MTI algorithms do not explicitly impose an a priori phase model, but nevertheless rely on some smoothness criteria in the temporal dimension to identify the stable pixels [3]. Clearly, then, the temporal coherence figure is not an exhaustive parameter to ascertain a posteriori the presence of useful information in a given MTI pixel time series, and it should be used with caution as a stable point detection criterion, as time series with low noise, following models different from the ones postulated in the detection step, will exhibit low coherence values, together with uninteresting, noisy time series. Moreover, one may be interested in discovering temporal trends which do not follow any of the predefined models used in the processing. 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. It should also be considered that MTI datasets are increasingly made available over wide areas, such as entire national [4, 5] and even continental scales, with computational loads which discourage extended use of a priori models more complex than the simplest ones. Thus, typically, additional tests have to be performed to recognize other "interesting" but non-modeled trends, and some automated approaches to this task have been proposed to date [6]. We propose here the fuzzy entropy (FuzEn), a quantity originally developed for medical time series analysis, as a viable parameter to characterize multi-temporal InSAR time series, in order to isolate smooth, or temporarily smooth trends without a predefined model. FuzEn [7] basically measures the degree of regularity of a given time series by comparing short sub-sequences of samples according to a given distance measure, typically the Chebyshev distance in the original formulation, which can be easily substituted by e.g. a distance defined on the circle to deal with possible unwrapping errors. Being a measure of disorder in a time series, FuzEn exhibits homogeneously low values for a large class of displacement models, such as seasonal, parabolic or piecewise linear signals, or series with a few discontinuities, while increasing for more chaotic trends, dominated by noise. It appears therefore suited as a model-free discriminative parameter to isolate a few meaningful MTI pixels time series within large datasets. It also exhibits good potential as an a priori criterion for stable scatterer detection. The calculation of FuzEn has low computational cost and can thus be easily performed in batch, as a pre-screening filter. In the presentation, some results over simulated data and some examples on a real dataset are shown, with interesting performances which hint to possible large-scale implementations. References [1] M. Crosetto, O. Monserrat, M. Cuevas-González, N. Devanthéry, G. Luzi, and B. Crippa, "Measuring thermal expansion using X-band persistent scatterer interferometry," ISPRS J. Photogramm. Remote. Sens., vol. 100, pp. 84-91, may 2015. [2] Y. Morishita and R. F. Hanssen, "Deformation Parameter Estimation in Low Coherence Areas Using a Multisatellite InSAR Approach," IEEE Transactions on Geosci. Remote. Sens., vol. 53, no. 8, pp. 4275-4283, 2015. [3] P. Berardino, G. Fornaro, R. Lanari, and E. Sansosti, "A new algorithm for surface deformation monitoring based on small baseline differential SAR interferograms," IEEE Transactions on Geosci. Remote. Sens., vol. 40, no. 11, pp. 2375-2383, 2002. [4] M. Caro Cuenca, R. F. Hanssen, A. J. Hooper, and M. Arikan, "Surface deformation of the whole Netherlands after PSI analysis," in FRINGE Workshop Proceedings, pp. 1-27, 2013. [5] M. Costantini, et al., "Analysis of surface deformations over the whole Italian territory by interferometric processing of ERS, Envisat and COSMO-SkyMed radar data," Remote. Sens. Environ., vol. 202, pp. 250-275, dec 2017. [6] M. Berti, A. Corsini, S. Franceschini, and J. P. Iannacone, "Automated classification of Persistent Scatterers Interferometry time series," Natural Hazards and Earth System Science, vol. 13, no. 8, pp. 1945-1958, Aug. 2013. [7] Weiting Chen, Zhizhong Wang, Hongbo Xie, and Wangxin Yu, "Characterization of Surface EMG Signal Based on Fuzzy Entropy," IEEE Transactions on Neural Syst. Rehabil. Eng., vol. 15, no. 2, pp. 266-272, 2007.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
