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Optimal shrinkage of singular values under high-dimensional noise with separable covariance structure

Pei-Chun SuHau-Tieng Wu
Jul 2022
摘要
We consider an optimal shrinkage algorithm that depends on an effective rankestimation and imputation, coined optimal shrinkage with imputation and rankestimation (OSIR), for matrix denoising in the presence of high-dimensionalnoise with the separable covariance structure (colored and dependent noise).The algorithm does not depend on estimating separable covariance structure ofthe noise. On the theoretical side, we study the asymptotic behavior of outliersingular values and singular vectors and prove the delocalization of thenon-outlier singular vectors of the associated random matrix with a convergencerate, and apply these results to analyze OSIR over different signal strengthsand sizes of data matrices. On the application side, we carry out simulationsto demonstrate the effectiveness of OSIR, and apply it to study the fetalelectrocardiogram signal processing challenge and the two-dimensional randomtomography problem.
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