Atomic Representation


ATOMIC Representation

Here is a summarized Table about atomic representation. You can read the following paper for more details. If you use this Table please cite this article:
R. Kafieh, H. Rabbani, I. Selesnick, “Three Dimensional Data-Driven Multi-Scale Atomic Representation of Optical Coherence Tomography”, IEEE Transactions on Medical Imaging, vol. 34, no. 5, pp. 1042-1062, May 2015. Codes


Official website or online reference

Reference

Introduced in

parameters

Dimension

Transform name

 

 

http://www.thefouriertransform.com

G. Campbell and R. Foster[16]

1948

Frequency

1D/2D/3D

Fourier Transform

Single Scale

Parametric methods

(non-data-driven dictionary)

http://planetmath.org/?op=getobj&from=objects&id=1469

N. Ahmed,

T. Natarajan

and K. R. Rao[17]

1974

Duration-Translation

1D/2D/3D

Cosine  Transform (DCT)

https://www.ceremade.dauphine.fr/~peyre/numerical-tour/tours/wavelet_4_daubechies2d/

I. Daubechies[18]

1988

Scale-Translation

1D/2D/3D

Separable Wavelet Transform

Multi-scale

http://www.bearcave.com/misl/misl_tech/wavelets/packet/index.html

R.R. Coifman[19]

1992

Scale-Translation- Frequency

1D/2D/3D

Wavelet  packet Transform

http://ssli.ee.washington.edu/people/duh/projects/wedgelets.html

D. L. Donoho[20]

1997

Scale-Translation- Rotation

2D

Geometrical X-lets (wedgelet)

http://eeweb.poly.edu/iselesni/WaveletSoftware

N. G. Kingsbury[21]

1998

Scale-Translation- Rotation

2D/3D

Complex Wavelet Transform

http://www.curvelet.org

E. Candès

and D. Donoho[22]

2000

Scale-Translation- Rotation

2D/3D

Geometrical X-lets (curvelet)

http://www.cmap.polytechnique.fr/~peyre/bandelets

Le Pennec and

E. Mallat[23]

2004

Scale-Translation- Rotation

2D

Geometrical X-lets (bandlet)

http://www.ifp.uiuc.edu/~minhdo/software/contourlet_toolbox.zip

MN. Do

and M. Vetterli[24]

2005

Scale-Translation- Rotation

2D

Geometrical X-lets (contourlet)

http://www.math.wustl.edu/IllMoHAS/pdfs/yuelu.pdf

Y Lu and MN Do[25]

2005

Scale-Translation- Rotation

3D

Geometrical X-lets (Surfacelet)

http://www.fon.hum.uva.nl/praat/manual/Principal_component_analysis.html

I.T. Jolliffe[26]

1986

Eigen Vectors

1D/2D/3D

Principal Component Analysis (PCA)

Single scale

Non-parametric methods

(dictionary learning)

http://www.cs.helsinki.fi/u/ahyvarin/whatisica.shtml

P. Comon[9]

1994

Eigen Vectors

1D/2D/3D

Independent Component Analysis (ICA)

http://eprints.maths.ox.ac.uk/740/1/bah.pdf and

http://www.math.ucla.edu/~wittman/mani/

R.R. Coifman

and S. Lafon[11]

2006

Spectral

1D/2D/3D

Diffusion Maps

http://media.aau.dk/null_space_pursuits/2012/04/dictionary-learning-with-the-method-of-optimal-directions.html

K Engan and SO Aase[14]

1999

Duration-Translation

1D/2D/3D

Conventional Method of Optimal Directions (MOD)

http://www.cs.technion.ac.il/~elad/software/

M Aharon[15]

2006

Duration-Translation

1D/2D/3D

Conventional K-SVD

http://www.math.duke.edu/~mauro/diffusionwavelets.html

 

R. R. Coifman

and M. Maggioni[27]

2006

Scale-Spectral

1D/2D/3D

Diffusion wavelet

Multi-scale

https://sites.google.com/site/hosseinrabbanikhorasgani/research/atomic-representation

R.Kafieh and H. Rabbani and I. Selesnick

This work

Scale-Translation- Rotation

1D/2D/3D

Complex wavelet based K-SVD



This site was built using