Fourier-Bessel rotational invariant eigenimages

Zhizhen Zhao, Amit Singer

Research output: Contribution to journalArticlepeer-review

41 Scopus citations


We present an efficient and accurate algorithm for principal component analysis (PCA) of a large set of twodimensional 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 band limited 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.

Original languageEnglish (US)
Pages (from-to)871-877
Number of pages7
JournalJournal of the Optical Society of America A: Optics and Image Science, and Vision
Issue number5
StatePublished - May 2013

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics
  • Computer Vision and Pattern Recognition


  • (100.0100) Image processing
  • (100.3008) Image recognition, algorithms and filters
  • (180.0180) Microscopy


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