Mathieu Fauvel

Mathieu Fauvel

Whittaker smoother is a widely adopted solution to pre-process satellite image time series. Yet, two key limitations remain: the smoothing parameter must be tuned individually for each pixel, and the standard formulation assumes homoscedastic noise, imposing uniform smoothing across the temporal dimension. This paper addresses both limitations by casting the Whittaker smoother as a differentiable neural layer, in which the smoothing parameter is inferred by a neural network. The framework is further extended to handle heteroscedastic noise through a time-varying regularization, allowing the degree of smoothing to adapt locally along the time series. To enable large-scale processing, a sparse, memory-efficient, and fully differentiable implementation is proposed, exploiting the symmetric banded structure of the underlying linear system via Cholesky factorization. Benchmarks on GPU demonstrate that this implementation substantially outperforms standard dense linear solvers, both in speed and memory consumption. The approach is validated on SITS acquired over the French metropolitan territory between 2016 and 2024. Results confirm the feasibility of large-scale heteroscedastic Whittaker smoothing, though reconstruction differences with the homoscedastic baseline remain limited, suggesting that the transformer architecture used for smoothing parameter estimation may lack the temporal acuity needed to capture abrupt noise variations such as singleday cloud contamination.

M. Fauvel, A. Villa, J. Chanussot et al.

The classification of high dimensional data with kernel methods is considered in this article. Exploit- ing the emptiness property of high dimensional spaces, a kernel based on the Mahalanobis distance is proposed. The computation of the Mahalanobis distance requires the inversion of a covariance matrix. In high dimensional spaces, the estimated covariance matrix is ill-conditioned and its inversion is unstable or impossible. Using a parsimonious statistical model, namely the High Dimensional Discriminant Analysis model, the specific signal and noise subspaces are estimated for each considered class making the inverse of the class specific covariance matrix explicit and stable, leading to the definition of a parsimonious Mahalanobis kernel. A SVM based framework is used for selecting the hyperparameters of the parsimonious Mahalanobis kernel by optimizing the so-called radius-margin bound. Experimental results on three high dimensional data sets show that the proposed kernel is suitable for classifying high dimensional data, providing better classification accuracies than the conventional Gaussian kernel.