Difference between revisions of "2012Zhao Denoising"
(Created page with "== Citation == Zhao, Z. & Singer, A. Fourier-Bessel rotational invariant eigenimages J. Optical Soc. America A, 2012, 30, 871-877 == Abstract == We present an efficient and...") |
Amit Singer (talk | contribs) (→Abstract) |
||
| Line 5: | Line 5: | ||
== Abstract == | == Abstract == | ||
| − | We present an efficient and accurate algorithm for principal | + | 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 | |
| − | dimensional images, and, for each image, the set of its | ||
| − | |||
algorithm starts by expanding each image, originally given | algorithm starts by expanding each image, originally given | ||
on a Cartesian grid, in the Fourier-Bessel basis for | on a Cartesian grid, in the Fourier-Bessel basis for | ||
the disk. Because the images are essentially bandlimited in | the disk. Because the images are essentially bandlimited in | ||
the Fourier domain, we use a sampling criterion to | the Fourier domain, we use a sampling criterion to | ||
| − | truncate the Fourier-Bessel expansion such that the | + | 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 | |
| − | effect of aliasing. The constructed covariance matrix is | + | 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 | |
| − | block diagonal structure. PCA is efficiently done for each | ||
| − | |||
| − | detects more meaningful eigenimages and has improved | ||
| − | |||
a finite number of noisy images. | a finite number of noisy images. | ||
Revision as of 18:18, 16 July 2014
Citation
Zhao, Z. & Singer, A. Fourier-Bessel rotational invariant eigenimages J. Optical Soc. America A, 2012, 30, 871-877
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 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.
Keywords
Denoising, PCA, rotational invariant basis
Links
http://arxiv.org/abs/1211.1968
