Research map / Learning theory and algorithms / Matrix and tensor methods
Phase retrieval in high dimensions: Statistical and computational phase transitions
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the spectral distribution of the sensing matrix to determine the algorithmic weak-recovery threshold | G-VAMP for noiseless phase retrieval · Right-orthogonally or right-unitarily invariant sensing matrices | algorithmic weak-recovery threshold α_WR,Algo: (1+β/2)⟨λ⟩ν²/⟨λ²⟩ν | Mixed |
| Use column-orthogonal or column-unitary sensing instead of Gaussian sensing | G-VAMP for noiseless phase retrieval · Real phase retrieval | algorithmic weak-recovery threshold α_WR,Algo: 0.5 -> 1.5 | Hurt |
| Use column-orthogonal or column-unitary sensing instead of Gaussian sensing | G-VAMP for noiseless phase retrieval · Complex phase retrieval | algorithmic weak-recovery threshold α_WR,Algo: 1 -> 2 | Hurt |
| Account for sensing-matrix rank deficiency | Bayes-optimal estimation · Noiseless phase retrieval | information-theoretic full-recovery threshold α_FR,IT: β(1-ν({0})) | Mixed |
| Use a Gaussian signal prior and noiseless phase-retrieval channel to compute thresholds | G-VAMP and Bayes-optimal estimation · Noiseless phase retrieval with complex Gaussian sensing matrices | full-recovery threshold α: 2 -> \simeq 2.027 | Mixed |
| Use a Gaussian signal prior and noiseless phase-retrieval channel to compute thresholds | G-VAMP and Bayes-optimal estimation · Noiseless phase retrieval with complex column-unitary sensing matrices | full-recovery threshold α: 2 -> \simeq 2.265 | Mixed |
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