To Regularize or Not to Regularize: The Role of Positivity in Sparse Array Interpolation with a Single Snapshot

We study single-snapshot nested array interpolation with positive sources. The problem of sparse array interpolation is traditionally cast as a low-rank Toeplitz/Hankel matrix completion problem from partial observations. In recent work, we provided the first necessary and sufficient guarantees for nested array interpolation with real measurements in the rank minimization framework. In this work, we strengthen the sufficiency results by proving that in case of positive sources it is possible to interpolate the nested array by performing a simple convex feasibility search instead of solving a rank minimization problem. Simulations demonstrate that this framework is also effective for noisy measurements, and that noisy nested array interpolation outperforms ULA extrapolation.
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