Abstract: Highlights•We construct a 5-D whitened spatial-temporal patch-tensor without second-order statistics of non-targets, and provide a data foundation for the 5-D spatial–temporal completion model establishment.•Inspired by separable time and space, and the joint spatial-temporal ways, we design a spatial-temporal factor-based background estimation norm.•Considering local spatial-temporal knowledge and global information, we propose a Moreau envelope-derived sparsity estimation norm.•We establish a spatial-temporal factor-based completion model along with an effective Alternating Direction Method of Multipliers-based algorithm.
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