Thesis Defenses Seminar
Monday, April 3, 2023, 3:00pm, 359 Gross Hall
Pei-Chun Su (Duke University, Mathematics)
Denoising high dimensional dataset with complicated noise and its clinical applications
We present a novel algorithm, called eOptShrink, for denoising matrices in the presence of high-dimensional, colored, and dependent noise with a separable covariance structure. The algorithm is totally data-driven and does not require estimation of the covariance structure of the noise. We provide the asymptotic behavior of the singular values and singular vectors of the random matrix associated with the noisy data, including the sticking property of non-outlier singular values and the delocalization of non-outlier singular vectors with a convergence rate. These theoretical results provide guarantees for the eOptShrink algorithm with a convergence rate. eOptShrink is then applied for denoising of biomedical signals. We especially introduce the detail of the recovery of fetal electrocardiogram (ECG) for both the fetal heart rate analysis and morphological analysis of its waveform from one or two transabdominal maternal ECG channels.

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