可旋转主成分用于空间-频率局部化图像
Steerable Principal Components for Space-Frequency Localized Images
AI总结：
本文提出一种快速准确的方法，通过二维Prolate Spheroidal Wave Functions对图像进行展开，获取可旋转主成分，用于图像及其旋转的最优扩展。
摘要：
本文描述了一种快速且准确的方法，用于从大量图像数据集中获得可旋转主成分，假设图像在空间和频率上具有良好的局部化特性。所获得的可旋转主成分用于图像数据集及其旋转的最优扩展。该方法首先使用一系列二维Prolate Spheroidal Wave Functions对图像进行展开，其中展开系数通过特殊设计的数值积分方案进行评估。然后，利用这些展开系数构建一个旋转不变的协方差矩阵，其具有块对角结构，其块的特征分解提供了所需的可旋转主成分。所提出的方法被证明比现有方法更快，同时提供适当的误差界以保证其准确性。
英文摘要：
This paper describes a fast and accurate method for obtaining steerable principal components from a large dataset of images, assuming the images are well localized in space and frequency. The obtained steerable principal components are optimal for expanding the images in the dataset and all of their rotations. The method relies upon first expanding the images using a series of two-dimensional Prolate Spheroidal Wave Functions (PSWFs), where the expansion coefficients are evaluated using a specially designed numerical integration scheme. Then, the expansion coefficients are used to construct a rotationally-invariant covariance matrix which admits a block-diagonal structure, and the eigen-decomposition of its blocks provides us with the desired steerable principal components. The proposed method is shown to be faster then existing methods, while providing appropriate error bounds which guarantee its accuracy.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
