Whittaker-Henderson Smoother for Long Satellite Image Time Series Interpolation
Summary: arXiv:2604.00048v1 Announce Type: cross
Abstract
The Whittaker smoother has emerged as a prominent method for pre-processing satellite image time series. However, two significant limitations hinder its performance: the requirement to individually tune the smoothing parameter for each pixel and the assumption of homoscedastic noise, which mandates uniform smoothing throughout the temporal dimension. This paper explores solutions to these challenges by reformulating the Whittaker smoother as a differentiable neural layer. In this innovative framework, a neural network infers the smoothing parameter, thus eliminating the need for manual tuning.
Key Innovations
The study introduces several key advancements in the application of the Whittaker smoother:
- Neural Network Inference: The smoothing parameter is dynamically inferred by a neural network, allowing for more accurate and context-sensitive smoothing across various pixels.
- Heteroscedastic Noise Handling: The framework is extended to accommodate heteroscedastic noise through a time-varying regularization. This capability enables the degree of smoothing to adapt locally throughout the time series, addressing variations in noise characteristics.
- Memory-Efficient Implementation: A sparse and fully differentiable implementation is proposed, leveraging the symmetric banded structure of the underlying linear system via Cholesky factorization. This implementation is designed for large-scale processing while maintaining efficiency in memory usage.
Performance Evaluation
Benchmarks conducted on GPU demonstrate that the proposed implementation significantly outperforms standard dense linear solvers in both speed and memory consumption. These enhancements are critical for handling extensive satellite image datasets, which are commonplace in remote sensing and environmental monitoring.
Validation and Results
The approach was validated on satellite image time series (SITS) acquired over the French metropolitan territory from 2016 to 2024. The results affirm the feasibility of large-scale heteroscedastic Whittaker smoothing, showcasing its potential for real-world applications in satellite image processing.
Conclusion
While the new method exhibits notable improvements, reconstruction differences from the homoscedastic baseline are observed to be limited. This suggests that the transformer architecture employed for smoothing parameter estimation may not possess the temporal precision necessary to effectively capture abrupt noise variations, such as single-day cloud contamination. Further research is warranted to enhance the model’s sensitivity to such variations, potentially leading to more robust and reliable satellite image time series interpolation.