  This paper proposes a novel spatiotemporal (ST) fusion framework for
satellite images, named Robust Optimization-based Spatiotemporal Fusion
(ROSTF). ST fusion is a promising approach to resolve a trade-off 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. Specifically, first, we define observation models for satellite images
possibly contaminated with random noise, outliers, and/or missing values, and
then introduce certain assumptions that would 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 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.
