Robust Low-Rank Change Detection for Multivariate SAR Image Time Series

Mian, Ammar; Collas, Antoine; Breloy, Arnaud; Ginolhac, Guillaume; Ovarlez, Jean‐Philippe

doi:10.1109/jstars.2020.2999615

Cited by 6 publications

(1 citation statement)

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“…The hypothesis of known σ 2 simplifies the exposition and does not change significantly the performance in practice when compared to a joint estimation scheme (see e.g. [23]). Without loss of generality, such assumption allows us to set σ 2 = 1.…”

Section: A Heteroscedastic Signal Modelmentioning

confidence: 99%

Probabilistic PCA From Heteroscedastic Signals: Geometric Framework and Application to Clustering

Collas¹,

Bouchard²,

Breloy³

et al. 2021

IEEE Trans. Signal Process.

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This paper studies a statistical model for heteroscedastic (i.e., power fluctuating) signals embedded in white Gaussian noise. Using the Riemannian geometry theory, we propose an unified approach to tackle several problems related to this model. The first axis of contribution concerns parameters (signal subspace and power factors) estimation, for which we derive intrinsic Cramér-Rao bounds and propose a flexible Riemannian optimization algorithmic framework in order to compute the maximum likelihood estimator (as well as other cost functions involving the parameters). Interestingly, the obtained bounds are in closed forms and interpretable in terms of problem's dimensions and SNR. The second axis of contribution concerns the problem of clustering data assuming a mixture of heteroscedastic signals model, for which we generalize the Euclidean K-means++ to the considered Riemannian parameter space. We propose an application of the resulting clustering algorithm on the Indian Pines segmentation problem benchmark.

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Section: A Heteroscedastic Signal Modelmentioning

confidence: 99%