Whittaker-Henderson smoother for long satellite image time series interpolation

2026-03-30

AI Summary

This work addresses the limitations of the traditional Whittaker smoother, which relies on manual parameter tuning and assumes homoscedastic noise, rendering it ill-suited for long time series with locally heteroscedastic noise. The authors reformulate the smoother as a differentiable neural network layer, leveraging a Transformer architecture to automatically estimate time-varying smoothing parameters and incorporating time-varying regularization for adaptive smoothing. The proposed method integrates differentiable optimization, Cholesky-accelerated sparse solvers, and GPU-based parallel computation, enabling end-to-end training and scalable processing of large-scale remote sensing data. Evaluated on nationwide French satellite time series from 2016 to 2024, the approach demonstrates substantial improvements in computational efficiency and memory performance, though it remains limited in modeling abrupt noise such as single-day cloud contamination.

Abstract

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.

Problem

• Whittaker smoother
• heteroscedastic noise
• satellite image time series
• smoothing parameter
• time-varying regularization

Innovation

• differentiable Whittaker smoother
• heteroscedastic noise
• time-varying regularization
• sparse Cholesky factorization
• neural parameter inference