# Spiked Covariance Estimation from Modulo-Reduced Measurements

@article{Romanov2022SpikedCE, title={Spiked Covariance Estimation from Modulo-Reduced Measurements}, author={Elad Romanov and Or Ordentlich}, journal={ArXiv}, year={2022}, volume={abs/2110.01150} }

Consider the rank-1 spiked model: X = √ νξ u + Z , where ν is the spike in-tensity, u ∈ S k − 1 is an unknown direction and ξ ∼ N (0 , 1) , Z ∼ N ( 0 , I ) . Motivated by recent advances in analog-to-digital con-version, we study the problem of recovering u ∈ S k − 1 from n i.i.d. modulo-reduced measurements Y = [ X ] mod ∆ , focusing on the high-dimensional regime ( k (cid:29) 1 ). We develop and analyze an algorithm that, for most directions u and ν = poly( k ) , estimates u to high accuracy…

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