For circular translations, MTD in high noise needs Θ(σ^6) samples; SO(2) rotations get a lower bound and translation-free gets an upper bound.
Multireference alignment is easier with an aperiodic translation distribution
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A note on the sample complexity of multi-target detection
For circular translations, MTD in high noise needs Θ(σ^6) samples; SO(2) rotations get a lower bound and translation-free gets an upper bound.