sePCA

sePCA estimates rotationally invariant covariance matrices and principal components from 2-D images with Poisson-distributed pixel intensities to support analyses such as XFEL single-molecule imaging and 3-D molecular structure reconstruction.

Key Features:

• Steerable ePCA: Integrates ePCA for exponential-family distributions with steerable PCA to produce principal components invariant to planar rotations and reflections.
• ePCA for exponential-family distributions: Extends PCA to handle Poisson-distributed pixel intensities and corrects bias of classical sample covariance estimators under photon-count noise.
• Steerable PCA: Incorporates all planar rotations of input images into the analysis to enforce rotational and reflection invariance of components.
• Covariance estimation from photon-limited images: Estimates covariance matrices from 2-D images affected by photon count noise for improved downstream structure reconstruction.
• Validation datasets: Demonstrated on simulated XFEL datasets and rotated face images from the Yale Face Database B.

Scientific Applications:

• XFEL single-molecule imaging: Provides rotationally invariant covariance estimates and principal components used for 3-D molecular structure reconstruction from 2-D diffraction images.
• Photon-limited image analysis: Corrects covariance-estimation bias in low-photon-count imaging scenarios characterized by Poisson noise.
• Algorithm validation on rotated images: Evaluates rotational and reflection invariance and covariance recovery using rotated face images from the Yale Face Database B.

Methodology:

Combines steerable ePCA, which merges ePCA for exponential-family (Poisson) data with steerable PCA that includes all planar rotations and reflections, to estimate covariance matrices and principal components from photon-limited 2-D images.