Fourier-Bessel rotational invariant eigenimages

TL;DR

This paper introduces a Fourier-Bessel basis-based PCA method for 2D images that is invariant to rotation and reflection, improving eigenimage detection and denoising over traditional PCA.

Contribution

The paper presents an efficient Fourier-Bessel PCA algorithm that handles large image sets with rotation and reflection invariance, enhancing eigenimage quality and noise reduction.

Findings

Detects more meaningful eigenimages

Improves denoising capabilities

Efficiently handles large datasets

Abstract

We present an efficient and accurate algorithm for principal component analysis (PCA) of a large set of two dimensional images, and, for each image, the set of its uniform rotations in the plane and its reflection. The algorithm starts by expanding each image, originally given on a Cartesian grid, in the Fourier-Bessel basis for the disk. Because the images are bandlimited in the Fourier domain, we use a sampling criterion to truncate the Fourier-Bessel expansion such that the maximum amount of information is preserved without the effect of aliasing. The constructed covariance matrix is invariant to rotation and reflection and has a special block diagonal structure. PCA is efficiently done for each block separately. This Fourier-Bessel based PCA detects more meaningful eigenimages and has improved denoising capability compared to traditional PCA for a finite number of noisy images.