Spatio‐temporal signal recovery under diffusion‐induced smoothness and temporal correlation priors

In this work, the signal recovery problem regarding incomplete and noisy spatio‐temporal signals is studied. A spatio‐temporal signal is considered as a time‐varying graph signal and a diffusion‐induced first‐order Markov signal model is developed to incorporate both the spatial structure and temporal correlation into the underlying graph. With this model, prior knowledge on spatial smoothness and temporal correlation is revisited, and the connections between the graph structure and differential temporal smoothness are revealed. The authors then accordingly formulate a spatio‐temporal signal recovery method by jointly exploiting the spatial smoothness, low rank and refined differential temporal smoothness. The formulated recovery problem is solved by a block coordinate descent‐based algorithm, which iteratively optimises the recovery accuracy and temporal correlation matrix. The experiments on three real‐world datasets reveal the high signal recovery accuracy of the proposed algorithm.