Steerable ePCA: Rotationally Invariant Exponential Family PCA
Steerable ePCA: Rotationally Invariant Exponential Family PCA
复制标题
DOI：
10.1109/tip.2020.2988139
复制
发表时间：
2018-12
影响因子：
10.6
通讯作者：
Zhizhen Zhao;Lydia T. Liu;A. Singer
中科院分区：
文献类型：
--
作者：
Zhizhen Zhao;Lydia T. Liu;A. Singer
在光子受限成像中，像素强度受到光子计数噪声的影响。许多应用需要对底层2-D清洁图像的协方差进行准确估计。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被用来重建三维分子结构。从低光子计数图像中准确估计协方差必须考虑像素强度服从泊松分布，因此经典的样本协方差估计器具有很强的偏差。此外，在单分子成像中，包含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精度。本文介绍了一种高效、准确的计数噪声二维图像协方差矩阵估计算法，该算法包括图像的均匀平面旋转和可能的反射。我们的程序，可转向$e$PCA，以一种新颖的方式结合了最近引入的两项创新。第一种是泊松分布的主成分分析(PCA)方法，更广泛地说，是指数族分布的主成分分析方法，称为$e$PCA。第二种是可导向的主元分析，这是一种在执行主元分析时包含所有平面旋转的快速而准确的过程。得到的主分量对于输入图像的旋转和反射是不变的。在模拟XFEL数据集和Yale人脸数据库B的旋转人脸图像上的数值实验中，我们证明了可定向的$e$PCA的有效性和准确性。
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.