We develop a novel filtering algorithm for remote sensing inverse problems that exploits sparsity in the precision (inverse covariance) matrix arising from conditional independence structures in spatio-temporal satellite data. Motivated by NASA's Orbiting Carbon Observatory-2 (OCO-2), Earth Surface Mineral Dust Source Investigation (EMIT), and upcoming Explorer for Artemis Geology Lunar and Earth (EAGLE) missions, we formulate a Bayesian inference framework for retrieving atmospheric and surface parameters from hyperspectral radiance measurements. Unlike traditional methods that operate on covariances and ignore spatio-temporal dependencies, our approach models the full spatio-temporal state using sparse Gaussian graphical models, which corresponds to a block-sparse precision matrix. We derive an information filter based on this structure, enabling scalable joint inference over large spatial grids with uncertainty propagation. We demonstrate the effectiveness of the algorithm in two distinct remote sensing contexts. First, we apply the method to synthetic data configured to mimic the OCO-2 mission, focusing on retrievals of atmospheric CO$_2$, and observe a 50% reduction in CO$_2$ retrieval error compared to single-pixel methods. Then, we evaluate the algorithm using imaging spectroscopy data from the Surface Biology and Geology (SBG) High Frequency Time Series (SHIFT) campaign to retrieve surface reflectance, achieving a 20% reduction in retrieval error relative to baseline approaches.

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