On the Performance of the SPICE Method

This letter considers the performance of the SPICE method in the context of line spectrum estimation by exploiting its equivalent square-root lasso (SR-LASSO) representation established in previous work. The inefficiencies of existing analyses are that the guarantees are not applicable to deterministic Fourier measurement matrices, and the studied range of the tuning parameter excludes the SR-LASSO formulation of the SPICE method. The key observation of this letter is that, for a particular range of tuning parameter, the solutions which overfit the noisy measurements are valid SR-LASSO solutions. Based on this observation, we propose to analyze these overfitting solutions and derive the condition of exact on-grid source localization that is applicable to the SPICE method. The numerical experiments demonstrate our theoretical claims.