Title: Optimal generalized tensor estimation with applications to 4D-STEM image denoising
Authors: Anru Zhang - Duke University (United States) [presenting]
Abstract: A general framework is introduced for generalized low-rank tensor learning problems, which includes many important instances arising from applications in computational imaging, genomics, network analysis, etc. To overcome the difficulty of non-convexity in these problems, we introduce a unified tensor approach that adapts to the underlying low-rank structure. Under mild conditions of rank-restricted convexity and smoothness on the loss function, we establish the upper bound on the statistical error and the linear rate of computational convergence through a general deterministic analysis. Then we further consider a suite of generalized tensor learning problems, including Gaussian tensor denoising, Poisson, binomial tensor PCA, and linear regression. Next, we apply the proposed approach to 4D-Scanning Transmission Electron Microscopy (4D-STEM) imaging analysis. For the 4D-STEM imaging data, due to the substantial noise brought up by photon-limited imaging technique, adequate and sufficient denoising often becomes the crucial first step in the analysis. Through the proposed tensor-based methods, we are able to achieve significantly better denoising performance and obtain smaller image reconstruction errors compared to the classic matrix-based denoising methods.