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 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, called ePCA. 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 ePCA in numerical experiments involving simulated XFEL datasets and rotated face images from Yale Face Database B.

中文翻译：

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可转向的ePCA：旋转不变指数族PCA。

在光子受限成像中，像素强度受光子计数噪声的影响。许多应用程序需要准确地估算基础2-D干净图像的协方差。例如，在X射线自由电子激光（XFEL）单分子成像中，二维衍射图像的协方差矩阵用于重构3-D分子结构。从低光子数图像中准确估计协方差必须考虑像素强度是泊松分布，因此经典样本协方差估算器存在很大偏差。此外，在单分子成像中，包括所有图像的面内旋转副本可以进一步提高协方差估计的准确性。在本文中，我们介绍了一种用于计数噪声二维图像协方差矩阵估计的高效准确算法，包括它们均匀的平面旋转和可能的反射。我们的过程，可操纵的ePCA，以新颖的方式结合了两个最新引入的创新。第一种是用于Poisson分布的主成分分析（PCA）的方法，更普遍的是称为ePCA的指数族分布。第二种是可操纵的PCA，这是执行PCA时包括所有平面旋转的快速而准确的过程。所得的主分量对于输入图像的旋转和反射是不变的。我们在涉及模拟XFEL数据集和来自Yale Face Database B的旋转面部图像的数值实验中证明了可控ePCA的效率和准确性。第一种是用于Poisson分布的主成分分析（PCA）的方法，更普遍的是称为ePCA的指数族分布。第二种是可操纵的PCA，这是执行PCA时包括所有平面旋转的快速而准确的过程。所得的主分量对于输入图像的旋转和反射是不变的。我们在涉及模拟XFEL数据集和来自Yale Face Database B的旋转面部图像的数值实验中证明了可控ePCA的效率和准确性。第一种是用于Poisson分布的主成分分析（PCA）的方法，更普遍的是称为ePCA的指数族分布。第二种是可操纵的PCA，这是执行PCA时包括所有平面旋转的快速而准确的过程。所得的主分量对于输入图像的旋转和反射是不变的。我们在涉及模拟XFEL数据集和来自Yale Face Database B的旋转面部图像的数值实验中证明了可控ePCA的效率和准确性。所得的主分量对于输入图像的旋转和反射是不变的。我们在涉及模拟XFEL数据集和来自Yale Face Database B的旋转面部图像的数值实验中证明了可控ePCA的效率和准确性。所得的主分量对于输入图像的旋转和反射是不变的。我们在涉及模拟XFEL数据集和来自Yale Face Database B的旋转面部图像的数值实验中证明了可控ePCA的效率和准确性。