2012Zhao Denoising - Revision history

Amit Singer: /* Related software */

2014-07-16T18:22:54Z

Related software

← Older revision		Revision as of 18:22, 16 July 2014
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	== Related software ==		== Related software ==

			ASPIRE

	== Related methods ==		== Related methods ==

	== Comments ==		== Comments ==

Amit Singer: /* Links */

2014-07-16T18:22:34Z

Links

← Older revision		Revision as of 18:22, 16 July 2014
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	== Links ==		== Links ==

	http://~~arxiv~~.~~org~~/~~abs~~/~~1211.1968~~		http://www.ncbi.nlm.nih.gov/pubmed/23695317

	== Related software ==		== Related software ==

Amit Singer: /* Abstract */

2014-07-16T18:18:51Z

Abstract

← Older revision		Revision as of 18:18, 16 July 2014
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	== Abstract ==		== Abstract ==

	We present an efficient and accurate algorithm for principal component analysis (PCA) of a large set of two-		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 uniform rotations in the plane and its reflection. The
	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

Amit Singer: /* Abstract */

2014-07-16T18:18:10Z

Abstract

← Older revision		Revision as of 18:18, 16 July 2014
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	== Abstract ==		== Abstract ==

	We present an efficient and accurate algorithm for principal c		We present an efficient and accurate algorithm for principal component analysis (PCA) of a large set of two-
	~~omponent~~ 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 ~~unifo~~
	rm rotations in the plane and its reflection. The
	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 ~~maximu~~		truncate the Fourier-Bessel expansion such that the maximum amount of information is preserved without the
	m 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 ~~inv~~		block diagonal structure. PCA is efficiently done for each block separately. This Fourier-Bessel based PCA
	~~ariant~~ to rotation and reflection and has a special		detects more meaningful eigenimages and has improved denoising capability compared to traditional PCA for
	block diagonal structure. PCA is efficiently done for each ~~blo~~
	ck separately. This Fourier-Bessel based PCA
	detects more meaningful eigenimages and has improved ~~denoi~~
	~~sing~~ capability compared to traditional PCA for
	a finite number of noisy images.		a finite number of noisy images.

CoSS: 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..."

2013-05-20T08:30:02Z

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..."

New page

== 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 c
omponent analysis (PCA) of a large set of two-
dimensional images, and, for each image, the set of its unifo
rm 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 maximu
m amount of information is preserved without the
effect of aliasing. The constructed covariance matrix is inv
ariant to rotation and reflection and has a special
block diagonal structure. PCA is efficiently done for each blo
ck separately. This Fourier-Bessel based PCA
detects more meaningful eigenimages and has improved denoi
sing 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

== Related software ==

== Related methods ==

== Comments ==