English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In photon-limited imaging, the pixel intensities are affected by photon countnoise. Many applications, such as 3-D reconstruction using correlation analysisin X-ray free electron laser (XFEL) single molecule imaging, require anaccurate estimation of the covariance of the underlying 2-D clean images.Accurate estimation of the covariance from low-photon count images must takeinto account that pixel intensities are Poisson distributed, hence theclassical sample covariance estimator is sub-optimal. Moreover, in singlemolecule imaging, including in-plane rotated copies of all images could furtherimprove the accuracy of covariance estimation. In this paper we introduce anefficient and accurate algorithm for covariance matrix estimation of countnoise 2-D images, including their uniform planar rotations and possiblyreflections. Our procedure, steerable $e$PCA, combines in a novel way tworecently introduced innovations. The first is a methodology for principalcomponent analysis (PCA) for Poisson distributions, and more generally,exponential family distributions, called $e$PCA. The second is steerable PCA, afast and accurate procedure for including all planar rotations for PCA. Theresulting principal components are invariant to the rotation and reflection ofthe input images. We demonstrate the efficiency and accuracy of steerable$e$PCA in numerical experiments involving simulated XFEL datasets and rotatedYale B face data.

Steerable $e$PCA: Rotationally Invariant Exponential Family PCA