Robust Spatiotemporal Fusion of Satellite Images: A Constrained Convex Optimization Approach

This article proposes a novel spatiotemporal (ST) fusion framework for satellite images, named robust optimization-based ST fusion (ROSTF). ST fusion is a promising approach to resolve a tradeoff between the temporal and spatial resolution of satellite images. Although many ST fusion methods have been proposed, most of them are not designed to explicitly account for noise in observed images, despite the inevitable influence of noise caused by the measurement equipment and environment. Our ROSTF addresses this challenge by formulating noise removal and ST fusion as a unified optimization problem. First, we define observation models for satellite images that may be contaminated with random noise, outliers, and/or missing values. Next, we introduce certain assumptions that naturally hold between the observed images and the target high-resolution image. Then, based on these models and assumptions, we formulate the fusion problem as a constrained optimization problem and develop an efficient algorithm based on a preconditioned primal-dual splitting method (P-PDS) for solving the problem. The performance of ROSTF was verified using simulated and real data. The results show that ROSTF performs comparably to several state-of-the-art ST fusion methods in noiseless cases and outperforms them in noisy cases.