# Whittaker-Henderson smoother for long satellite image time series interpolation

arXiv: https://arxiv.org/abs/2604.00048 · HTML: https://mlsanity.com/paper/2604.00048/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 20 references that are in the map.
- First posted on arXiv 30 Mar 2026.

## Builds on (most cited first, 4 of 4)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Divided Differences, Falling Factorials, and Discrete Splines: Another Look at Trend Filtering and Related Problems](https://mlsanity.com/paper/2003.03886/) (2020)
- [Whittaker--Henderson smoothing revisited: A modern statistical framework for practical use](https://mlsanity.com/paper/2306.06932/) (2023)

## Built on by (most cited first, 1 of 1)

- [Densification and forecasting of Sentinel-2 time series from multimodal SAR and Optical satellite data using deep generative models](https://mlsanity.com/paper/2605.04239/) (2026)

## Abstract (arXiv)

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.