Spatiotemporal satellite data imputation using sparse functional data analysis

Abstract

Many scientific applications and signal processing algorithms require complete satellite images. However, missing data in satellite images is very common due to various reasons such as cloud cover and sensor-specific problems. This paper introduces a general spatiotemporal satellite image imputation method based on sparse functional data analytic techniques. To handle observations consisting of a few longitudinally repeated satellite images that are themselves partially observed and noise-contaminated, we propose a multistep imputation method by following the best linear unbiased prediction principle and pooling information across all available locations and time points. Theoretical properties are established for the proposed approach under a new observation model for functional data that covers the dataset in question as a special case. Practical analysis on the Landsat data are conducted to illustrate and validate our algorithm which also shows that the proposed method considerably outperforms existing algorithms in terms of prediction accuracy. An efficient implementation using R and Rcpp is made available in the R package $\mathtt{stfit}$.