Steerable principal components for space-frequency localized images

Boris Landa*, Yoel Shkolnisky

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

As modern scientific image datasets typically consist of a large number of images of high resolution, devising methods for their accurate and efficient processing is a central research task. In this paper, we consider the problem of obtaining the steerable principal components of a dataset, a procedure termed “steerable PCA” (steerable principal component analysis). The output of the procedure is the set of orthonormal basis functions which best approximate the images in the dataset and all of their planar rotations. To derive such basis functions, we first expand the images in an appropriate basis, for which the steerable PCA reduces to the eigen-decomposition of a block-diagonal matrix. If we assume that the images are well localized in space and frequency, then such an appropriate basis is the prolate spheroidal wave functions (PSWFs). We derive a fast method for computing the PSWFs expansion coefficients from the images’ equally spaced samples, via a specialized quadrature integration scheme, and show that the number of required quadrature nodes is similar to the number of pixels in each image. We then establish that our PSWF-based steerable PCA is both faster and more accurate then existing methods, and more importantly, provides us with rigorous error bounds on the entire procedure.

Original languageEnglish
Pages (from-to)508-534
Number of pages27
JournalSIAM Journal on Imaging Sciences
Volume10
Issue number2
DOIs
StatePublished - 2017

Funding

FundersFunder number
The Israel Science FoundationR01GM090200, 578/14
National Institute of General Medical Sciences

    Keywords

    • Band limited functions
    • Group invariance
    • Principal component analysis
    • Prolate spheroidal wave functions
    • Steerable filters

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