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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可操纵 ePCA：旋转不变指数族 PCA


在光子限制成像中，像素强度受到光子计数噪声的影响。许多应用需要准确估计底层二维干净图像的协方差。例如，在 X 射线自由电子激光 (XFEL) 单分子成像中，2-D 衍射图像的协方差矩阵用于重建 3-D 分子结构。低光子计数图像的协方差的准确估计必须考虑到像素强度是泊松分布的，因此经典的样本协方差估计器是高度偏差的。此外，在单分子成像中，包括所有图像的平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，我们介绍了一种高效且准确的算法，用于计数噪声二维图像的协方差矩阵估计，包括它们的均匀平面旋转和可能的反射。我们的程序可操纵 ePCA 以新颖的方式结合了最近推出的两项创新。第一种是泊松分布（更一般而言，指数族分布）的主成分分析 (PCA) 方法，称为 ePCA。第二种是可操纵 PCA，这是一种快速而准确的程序，用于在执行 PCA 时包含所有平面旋转。所得的主成分对于输入图像的旋转和反射是不变的。我们在涉及模拟 XFEL 数据集和来自耶鲁人脸数据库 B 的旋转人脸图像的数值实验中展示了可操纵 ePCA 的效率和准确性。