Geographically Weighted Spatial Unmixing for Spatiotemporal Fusion

Spatiotemporal fusion is a technique applied to create images with both fine spatial and temporal resolutions by blending images with different spatial and temporal resolutions. Spatial unmixing (SU) is a widely used approach for spatiotemporal fusion, which requires only the minimum number of input images. However, ignorance of spatial variation in land cover between pixels is a common issue in existing SU methods. For example, all coarse neighbors in a local window are treated equally in the unmixing model, which is inappropriate. Moreover, the determination of the appropriate number of clusters in the known fine spatial resolution image remains a challenge. In this article, a geographically weighted SU (SU-GW) method was proposed to address the spatial variation in land cover and increase the accuracy of spatiotemporal fusion. SU-GW is a general model suitable for any SU method. Specifically, the existing regularized version and soft classification-based version were extended with the proposed geographically weighted scheme, producing 24 versions (i.e., 12 existing versions were extended to 12 corresponding geographically weighted versions) for SU. Furthermore, the cluster validity index of Xie and Beni (XB) was introduced to determine automatically the number of clusters. A systematic comparison between the experimental results of the 24 versions indicated that SU-GW was effective in increasing the prediction accuracy. Importantly, all 12 existing methods were enhanced by integrating the SU-GW scheme. Moreover, the identified most accurate SU-GW enhanced version was demonstrated to outperform two prevailing spatiotemporal fusion approaches in a benchmark comparison. Therefore, it can be concluded that SU-GW provides a general solution for enhancing spatiotemporal fusion, which can be used to update existing methods and future potential versions.