We present an efficient and accurate algorithm for principal componentanalysis (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 algorithmstarts by expanding each image, originally given on a Cartesian grid, in theFourier-Bessel basis for the disk. Because the images are bandlimited in theFourier domain, we use a sampling criterion to truncate the Fourier-Besselexpansion such that the maximum amount of information is preserved without theeffect of aliasing. The constructed covariance matrix is invariant to rotationand reflection and has a special block diagonal structure. PCA is efficientlydone for each block separately. This Fourier-Bessel based PCA detects moremeaningful eigenimages and has improved denoising capability compared totraditional PCA for a finite number of noisy images.
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