Steerable Principal Components for Space-Frequency Localized Images

TL;DR

This paper introduces a fast, accurate method for deriving steerable principal components from space-frequency localized images, leveraging PSWFs and a block-diagonal covariance matrix for efficient computation.

Contribution

The paper presents a novel approach combining PSWFs and a specialized numerical scheme to efficiently compute steerable principal components with guaranteed accuracy.

Findings

Method is faster than existing approaches.

Provides error bounds ensuring accuracy.

Effective for large datasets of localized images.

Abstract

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.