2012Zhao Denoising: Difference between revisions
(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) |
||
| (3 intermediate revisions by the same user not shown) | |||
| 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. | ||
| Line 29: | Line 22: | ||
== Links == | == Links == | ||
http:// | http://www.ncbi.nlm.nih.gov/pubmed/23695317 | ||
== Related software == | == Related software == | ||
ASPIRE | |||
== Related methods == | == Related methods == | ||
== Comments == | == Comments == | ||
Latest revision as of 18:22, 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://www.ncbi.nlm.nih.gov/pubmed/23695317
Related software
ASPIRE