Varying-Time Random Effects Models for Longitudinal Data: Spatial Disaggregation and Temporal Interpolation of Remote Sensing Data

Overview & Synopsis

Remote sensing is an helpful tool for crop monitoring or vegetation growth estimation at a country or regional scale. However, satellite images generally have to cope with a compromise between the time frequency of observations and their resolution (i.e. pixel size). When concerned with high temporal resolution, we have to work with information on the basis of kilometric pixels that represent aggregated responses of multiple land cover inside each low resolution pixel. Disaggreggation is then necessary to downscale from the square kilometer to the local dynamic of each parcel (crop, wood, meadows,...). We propose to address this question through the generalisation of varying-time regression models for longitudinal data and/or functional data by introducing local mixed effects. The estimators are built by expanding the mixed pixels trajectories with B-splines functions and maximizing the log-likelihood with a Backfitting-ECME algorithm. A BLUP formula allows then to get the "best possible" estimations of the local temporal responses of each crop when observing mixed pixels trajectories. We show that this model has many potential applications in remote sensing and an interesting one consists in coupling high and low spatial resolution images in order to perform temporal interpolation of high spatial resolution images (20m), increasing the knowledge on particular crops in very precise locations. The disaggregation, or downscaling, and interpolation approaches are illustrated on remote sensing data obtained on the South-Western of France during the year 2002.