PARSIMONY, HUGE OBSERVATIONS OF EARTH NON-STATIONARITIES FROM IMAGES TIME SERIES – PHOENIX

PHOENIX is divided in 3 work packages denoted WP1, WP2 and WP3. WP1 (parametric modeling) and WP2 (non-parametric methods) address methodological issues raised by the high geo-spatio-temporal dimensionality of the earth surface time series under consideration in the project. These methodological WPs are complementary and interconnected by construction.
WP1, “Generalized non-stationary models for random field time series” will perform the following tasks:
[T1-1] “Identification of a generalized spatio-temporal random field time series model” associated with the selection of a model encompassing non-stationarity, cyclicity, short term and long term spatio-temporal dependencies over random field time series.
[T1-2] “Development of estimation tools for computing the parameters of the parsimonious model” for hyperparameter estimation for random field time series models derived from T1-1.
Tasks associated with WP2 “Non-parametric random field time series analysis” are:
[T2-1] “Development of spatio-temporal cumulant analysis methods” associated with the derivation of non-parametric parsimony measures for the generalized model issued from T1-1;
[T2-2] “Non-parametric statistical analysis for random field time series decomposition” associated with the derivation of automatic methods for trend and stationary decompositions.
These fundamental prospective packages are expected to answer the issues of sequential change-detection, estimation and information fusion in high dimensional functional spaces. The proposed methods can benefit to several application domains.
The applications addressed in the PHOENIX project are related to the temporal evolution of some dynamic earth surface features: Alpine glaciers and Amazonian forests. These applications are assigned to a third work package, WP3, dedicated to “earth observation by using satellite image time series”. This WP deals with the adaptation of the models and methods of WP1 and WP2 to the specificities of earth data.

A) Generalized fractional random fields

Reference [1] provides several models of generalized stochastic fields obtained from series of fractional order discrete 2D difference equations.

Reference [2] provides statistical properties of wavelet operators when the observation model can be seen as the product of a deterministic piecewise regular function (signal) and a stationary random field (noise). This multiplicative observation model is analyzed in two standard frameworks by considering either (1) a direct wavelet transform of the model or (2) a log-transform of the model prior to wavelet decomposition. The paper shows that, in Framework (1), wavelet coefficients of the time series are affected by intricate correlation structures which blur signal singularities. Framework (2) is shown to be associated with a multiplicative (or geometric) wavelet transform and the multiplicative interactions between wavelets and the model highlight both sparsity of signal changes near singularities (dominant coefficients) and decorrelation of speckle wavelet coefficients. The paper then derives that, for time series of synthetic aperture radar data, geometric wavelets represent a more intuitive and relevant framework for the analysis of smooth earth fields observed in the presence of speckle.

- Symbolic parsimonious representations
- Possibilist field models
- Random field image time series analysis

[1] A. M. Atto, Ondelettes et Processus Stochastiques, Ed. Lavoisier, Hermès Science Publications, ISBN : 9782746248007, 2017.
[2] A. M. Atto, E. Trouvé, J. M. Nicolas and T. T. Lê, Wavelet Operators and Multiplicative Observation Models—Application to SAR Image Time-Series Analysis, IEEE Transactions on Geoscience and Remote Sensing, vol. 54, no. 11, pp. 6606-6624, Nov. 2016.
[3] C. Lesniewska-Choquet, A. M. Atto, G. Mauris, G. Mercier, Image Change Detection by Possibility Distribution Dissemblance, IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), July 9-12, Naples, Italy, 2017.
[4] J.-P. Ovarlez, G. Ginolhac, A. M. Atto, Multivariate Linear Time-Frequency Modeling and Adaptive Robust Target Detection in Highly Textured Monovariate SAR Image, IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), March 5-9, New Orleans, USA, 2017.
[5] H. Hadhri, F. Vernier, A. M. Atto, E. Trouvé, Traitement automatique de «time lapse« : application à la surveillance de glaciers alpins, ORASIS, journées francophones des jeunes chercheurs en vision par ordinateur, Juin 12-16, Colleville-sur-Mer, France, 2017.

Environment monitoring is crucial for understanding the relationship between climate change and changes in large scale earth structures such as glaciers and forests. For these big structures, monitoring temporal evolution or assessing resilience and adaptation of earth to changes requires the analysis of time series composed of images.
When considering remote sensing imagery, analyzing such time series is actually facing dimensionality: observations are huge data both in time and space domains; in addition with intricacy when using coherent acquisition waves (radar imaging for instance). The challenge of remote sensing information science is then developing tools for handling dimensionality of data.
The scientific objective of the PHOENIX project is to provide non-stationary multidimensional models for easing information mining and retrieval in long sequences of multisource/distributed image time series issued from recent constellations of satellites. These models will be used to characterize the evolution of earth structures such as glaciers and forests.
The technical objective of the PHOENIX project is to provide resilience analysis from information modeling and retrieval in image time series of Alpine glaciers and Amazonian forests. This analysis will be performed through a general framework of random field time series, with two work packages (WP) dedicated to methodological developments. The first package, WP1, will address parsimonious parametric modeling of random field time series by using non-stationary fractionally differenced/integrated parameterizations. The second package, WP2, is dedicated to non-parametric methods for the analysis of random field time series: cumulant analysis and trend/stationary decompositions are some important topics addressed in this WP. The third package, WP3, will focus on the application of WP1 and WP2 methods to 2 kinds of mono/multi-channel earth observation satellite image time series: 1) Synthetic Aperture Radar images which cover large areas and are not impacted by meteorological variability, 2) Spectro-Visible images which can observe specific areas with a higher spatio-spectral resolution. WP3 requires High Performance Computing (HPC). HPC will deserve two types of architectures: a big cluster of CPU (USMB MUST, already operational, efficient for parallel computing on “large databases with small size data”, but limited for loading and processing huge data) and a specific scalable workstation with huge random access memory (ANR support requested) for loading and processing huge size image time series.