Noisy-case estimation-error bounds

Derive upper bounds on the estimation error of the polynomial-equation sparse-approximation approach in the presence of measurement noise using its connection with eigenvalue decomposition and canonical polyadic decomposition.

Background

The paper reformulates sparse approximation as a structured polynomial system and develops both an algebraic Macaulay method and optimization-based methods, SESP-D and SESP-P. Although the experiments evaluate recovery under additive noise and compare performance with an oracle estimator, no analytical upper bounds on the resulting estimation error are established.

The authors identify the connection with eigenvalue decomposition and canonical polyadic decomposition as a possible route toward deriving such bounds, leaving the problem unresolved.