Wavelet Operators and Multiplicative Observation Models - Application to Joint Change-Detection and Regularization of SAR Image Time Series
Résumé
This paper addresses the sparsity and stochasticity properties of wavelet transforms of speckled data, when these data are considered either with or without log-transform. The case where a log-transform is applied on multiplicative speckled data prior to wavelet transform is first associated with a framework of multiplicative (or geometric) wavelets. Then, through wavelet cumulant analysis, those multiplicative wavelets are shown to highlight both sparsity and stochasticity intrinsic to speckled data due to geometric differencing. In contrast, standard wavelet implementation (without log-transform) of speckled data yields intricate correlation structures which makes a clear separation between sparsity and stochasticity difficult, in particular for highly resolved data. The paper then derives that, for high resolution synthetic aperture radar data issued from airborne or new generation satellites, multiplicative wavelets represent a more relevant framework for the analysis of smooth earth fields observed in the presence of speckle. From this analysis, the paper derives a fast-and-concise multiplicative wavelet based method for joint change detection and regularization of synthetic aperture radar image time series. In this method, multiplicative wavelet details are first computed with respect to the temporal axis in order to derive change-images from the time series. The changes are then enhanced and speckle is attenuated by using sigmoid shrinkage functions. Finally, a regularized time series is reconstructed from the sigmoid shrunken change-images. An application to the analysis of RADARSAT-2 quad-polarimetric and SENTINEL-1A dual-polarimetric image time series over Chamonix-Mont-Blanc test site is proposed to show the relevancy and straightforwardness of the method.
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