  We study the multi-target detection problem of recovering a target signal
from a noisy measurement that contains multiple copies of the signal at unknown
locations. Motivated by the structure reconstruction problem in cryo-electron
microscopy, we focus on the high noise regime, where noise hampers accurate
detection of signal occurrences. Previous works proposed an autocorrelation
analysis framework to estimate the signal directly from the measurement,
without detecting signal occurrences. Specifically, autocorrelation analysis
entails finding a signal that best matches the observable autocorrelations by
minimizing a least squares objective. This paper extends this line of research
by developing a generalized autocorrelation analysis framework that replaces
the least squares by a weighted least squares. The optimal weights can be
computed directly from the data and guarantee favorable statistical properties.
We demonstrate signal recovery from highly noisy measurements, and show that
the proposed framework outperforms autocorrelation analysis in a wide range of
parameters.

Signal Processing