Unbiasing Procedures for Scale-Invariant Multi-Reference Alignment - IPAM at UCLA

Explore unbiasing procedures for scale-invariant multi-reference alignment in this 51-minute lecture by Anna Little from the University of Utah. Delve into the mathematical analysis of multi-reference alignment problems, focusing on recovering hidden signals from noisy observations. Examine the generalization of the classic problem by incorporating random dilations alongside random translations and additive noise. Discover multiple approaches to solving this challenging model based on translation invariant representations. Learn about wavelet-based unbiasing procedures for unknown dilation distributions and more accurate methods for known distributions. Investigate the convergence rates of estimators and their dependence on sample size and noise levels. Explore the application of signal processing tools in distribution learning from biased, sparse batches. Gain insights into cryoelectron microscopy challenges, wavelet transforms, and signal recovery techniques through theoretical discussions and numerical experiments.