Zhao, Z. & Singer, A. Fourier-Bessel rotational invariant eigenimages J. Optical Soc. America A, 2012, 30, 871-877
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 essentially 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.
Denoising, PCA, rotational invariant basis