Steerable ePCA: Rotationally Invariant Exponential Family PCA

Abstract

In photon-limited imaging, the pixel intensities are affected by photon count noise. Many applications, such as 3-D reconstruction using correlation analysis in X-ray free electron laser (XFEL) single molecule imaging, require an accurate estimation of the covariance of the underlying 2-D clean images. Accurate estimation of the covariance from low-photon count images must take into account that pixel intensities are Poisson distributed, rendering the sub-optimality of the classical sample covariance estimator. Moreover, in single molecule imaging, including in-plane rotated copies of all images could further improve the accuracy of covariance estimation. In this paper we introduce an efficient and accurate algorithm for covariance matrix estimation of count noise 2-D images, including their uniform planar rotations and possibly reflection. Our procedure, steerable ePCA, combines in a novel way two recently introduced innovations. The first is a methodology for principal component analysis (PCA) for Poisson distributions, and more generally, exponential family distributions [1], called ePCA. The second is steerable PCA [2], [3], a fast and accurate procedure for including all planar rotations for PCA. The resulting principal components are invariant to the rotation and reflection of the input images. We demonstrate the efficiency and accuracy of steerable ePCA in numerical experiments involving simulated XFEL datasets.Index Terms-Poisson noise, X-ray free electron laser, steerable PCA, eigenvalue shrinkage, autocorrelation analysis, image denoising.ZZ is with the

Matrix Denoising for Weighted Loss Functions and Heterogeneous Signals

“…While this paper has focused on theoretical and algorithmic development, in future work we plan to apply the methods to problems where related but suboptimal methods have previously been employed. This includes the problems of denoising and deconvolution of images from cryoelectron microscopy [8], three-dimensional reconstruction of heterogeneous molecules from noisy images [1], and denoising XFEL images [41,56].…”