Exact rank-two globally identifying optimum

Determine the exact optimum of the global-identification-constrained information objective for rank-two complex row-space projectors in the compressed single-tone frequency-estimation model with unknown complex gain.

Background

For output rank two, the paper determines the unconstrained information optimum: the symmetric endpoint plane uniquely maximizes the worst-frequency efficient-information functional, but its projective response is aliased. The paper also proves a positive lower bound on the information price required for global identification and exhibits globally identifying rank-two planes. However, the lower bound is not shown to be sharp, so the exact constrained optimum remains unresolved.

References

Open problems include the exact rank-two GI-constrained optimum, arbitrary-row-space values and attainment for proper residual odd ranks, the complete singular local limit experiment, exact minimax constants after fixing a leading normal form, and the transition as the gain annulus collapses.

Compressed Single-Tone Frequency Estimation With Unknown Complex Gain: Singular Rates and Global Identifiability  (2608.30623 - Rasooli, 31 Aug 2026) in Section 6, Discussion and Limits

Open problems include the exact rank-two GI-constrained optimum, arbitrary-row-space values and attainment for proper residual odd ranks, the complete singular local limit experiment, exact minimax constants after fixing a leading normal form, and the transition as the gain annulus collapses.

Compressed Single-Tone Frequency Estimation With Unknown Complex Gain: Singular Rates and Global Identifiability  (2608.30623 - Rasooli, 31 Aug 2026) in Section 6, Discussion and Limits

Open problems include the exact rank-two GI-constrained optimum, arbitrary-row-space values and attainment for proper residual odd ranks, the complete singular local limit experiment, exact minimax constants after fixing a leading normal form, and the transition as the gain annulus collapses.

Compressed Single-Tone Frequency Estimation With Unknown Complex Gain: Singular Rates and Global Identifiability  (2608.30623 - Rasooli, 31 Aug 2026) in Section 6, Discussion and Limits