Two-stage dimension reduction for noisy high-dimensional images and application to Cryogenic Electron Microscopy

TL;DR

This paper introduces a two-stage dimension reduction method for noisy high-dimensional images, combining tensor-based denoising with vectorization, and demonstrates its effectiveness on cryo-EM data with theoretical guarantees.

Contribution

The paper proposes a novel two-stage dimension reduction approach that improves image reconstruction from noisy high-dimensional data, with theoretical consistency and practical applications to cryo-EM.

Findings

2SDR outperforms traditional PCA in noisy image reconstruction

The method achieves accurate rank selection asymptotically

Applications to cryo-EM datasets show significant improvements

Abstract

Principal component analysis (PCA) is arguably the most widely used dimension-reduction method for vector-type data. When applied to a sample of images, PCA requires vectorization of the image data, which in turn entails solving an eigenvalue problem for the sample covariance matrix. We propose herein a two-stage dimension reduction (2SDR) method for image reconstruction from high-dimensional noisy image data. The first stage treats the image as a matrix, which is a tensor of order 2, and uses multilinear principal component analysis (MPCA) for matrix rank reduction and image denoising. The second stage vectorizes the reduced-rank matrix and achieves further dimension and noise reduction. Simulation studies demonstrate excellent performance of 2SDR, for which we also develop an asymptotic theory that establishes consistency of its rank selection. Applications to cryo-EM (cryogenic electronic microscopy), which has revolutionized structural biology, organic and medical chemistry, cellular and molecular physiology in the past decade, are also provided and illustrated with benchmark cryo-EM datasets. Connections to other contemporaneous developments in image reconstruction and high-dimensional statistical inference are also discussed.