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This paper investigates the problem of reconstructing  n -by- n  structured matrix signal via convex optimization. The traditional vector signal model is extended to matrix signal model. We establish fundamental conditions on the measurement operator to guarantee strong properties of sparse and flat matrix signal reconstruction from noisy measurements, i.e., conditions to guarantee uniqueness, support and sign stability as well as value-error robustness. In comparison with other works, these conditions are more general and our method is more suitable to be generalized to dealing with high-order tensor signals. These theoretical results, together with the auxiliary results in the argument, are heuristic for developing more effective algorithms in, e.g., wide-band communications and related signal processing applications.

On General Conditions for Uniqueness and Robustness of Structured Matrix Signal Reconstruction