TY - JOUR
T1 - Steerable ePCA
T2 - Rotationally Invariant Exponential Family PCA
AU - Zhao, Zhizhen
AU - Liu, Lydia T.
AU - Singer, Amit
N1 - Funding Information:
Manuscript received December 12, 2018; revised July 13, 2019, December 4, 2019, and February 25, 2020; accepted March 29, 2020. Date of publication April 27, 2020; date of current version May 1, 2020. The work of Zhizhen Zhao was supported in part by the National Center for Supercomputing Applications Faculty Fellowship, University of Illinois at Urbana–Champaign College of Engineering Strategic Research Initiative and in part by NSF under Grant DMS-1854791. The work of Amit Singer was supported in part by the NIGMS, under Award R01GM090200, in part by AFOSR under Grant FA9550-17-1-0291, in part by the Simons Investigator Award, in part by the Moore Foundation Data-Driven Discovery Investigator Award, and in part by the NSF BIGDATA Award under Grarnt IIS-1837992. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Giacomo Boracchi. (Corresponding author: Zhizhen Zhao.) Zhizhen Zhao is with the Department of Electrical and Computer Engineering, University of Illinois at Urbana–Champaign, Urbana, IL 61820 USA (e-mail: zhizhenz@illinois.edu).
Publisher Copyright:
© 1992-2012 IEEE.
PY - 2020
Y1 - 2020
N2 - In photon-limited imaging, the pixel intensities are affected by photon count noise. Many applications require an accurate estimation of the covariance of the underlying 2-D clean images. For example, in X-ray free electron laser (XFEL) single molecule imaging, the covariance matrix of 2-D diffraction images is used to reconstruct the 3-D molecular structure. Accurate estimation of the covariance from low-photon-count images must take into account that pixel intensities are Poisson distributed, hence the classical sample covariance estimator is highly biased. 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 reflections. Our procedure, steerable e PCA, 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, called e PCA. The second is steerable PCA, a fast and accurate procedure for including all planar rotations when performing PCA. The resulting principal components are invariant to the rotation and reflection of the input images. We demonstrate the efficiency and accuracy of steerable e PCA in numerical experiments involving simulated XFEL datasets and rotated face images from Yale Face Database B.
AB - In photon-limited imaging, the pixel intensities are affected by photon count noise. Many applications require an accurate estimation of the covariance of the underlying 2-D clean images. For example, in X-ray free electron laser (XFEL) single molecule imaging, the covariance matrix of 2-D diffraction images is used to reconstruct the 3-D molecular structure. Accurate estimation of the covariance from low-photon-count images must take into account that pixel intensities are Poisson distributed, hence the classical sample covariance estimator is highly biased. 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 reflections. Our procedure, steerable e PCA, 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, called e PCA. The second is steerable PCA, a fast and accurate procedure for including all planar rotations when performing PCA. The resulting principal components are invariant to the rotation and reflection of the input images. We demonstrate the efficiency and accuracy of steerable e PCA in numerical experiments involving simulated XFEL datasets and rotated face images from Yale Face Database B.
KW - Poisson noise
KW - X-ray free electron laser
KW - autocorrelation analysis
KW - eigenvalue shrinkage
KW - image denoising
KW - steerable PCA
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U2 - 10.1109/TIP.2020.2988139
DO - 10.1109/TIP.2020.2988139
M3 - Article
C2 - 32340944
AN - SCOPUS:85084435336
SN - 1057-7149
VL - 29
SP - 6069
EP - 6081
JO - IEEE Transactions on Image Processing
JF - IEEE Transactions on Image Processing
M1 - 9078828
ER -