Improving the Optimization Landscape of Matrix Completion with $\epsilon$-close Surrogates

The paper proposes a new approach to matrix completion by adding small (ε-level) perturbations to the nullspace of the observation mask, creating noisy surrogates that remain close to the true matrix. These surrogates satisfy a restricted isometry property, enabling the use of tensor methods with theoretical guarantees. The authors provide quantitative recovery guarantees under independent observation assumptions, without requiring explicit sampling rate or incoherence conditions.

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