On General Conditions for Uniqueness and Stability of Sparse Tensor Signal Reconstruction

This paper deals with a fundamental aspect of the inverse problem of robustly reconstructing sparse tensor signals via convex optimization. The traditional vector signal model is extended to tensor model and tensor-space based convex optimization methods are applied to establish the critical results. In particular, by means of some innovative sub-differential analysis for tensor norms and convex geometric analysis in normed tensor space, sufficient conditions to guarantee uniqueness and stability of sparse tensor signal reconstruction are established. In comparison with most current works based on vector signal model (1-order tensor), these conditions are more general and more applicable to tensor signals. Also will these conditions be helpful for establishing practical algorithms for reconstructing high-order sparse tensor signals which are emerging in various data-intensive intelligent applications.