Image Empirical Mode Decomposition
Anna Linderhed.

Contact : anna.linderhed "at" foi.se
change "at" to @

The Empirical Mode Decomposition (EMD) was revealed by Norden E. Huang. EMD is an adaptive decomposition with which any complicated signal can be decomposed into its Intrinsic Mode Functions (IMF). EMD is an analysis method that in many aspects gives a better understanding of the physics behind the signals. Because of its ability to describe short time changes in frequencies that can not be resolved by Fourier spectral analysis it can be used for nonlinear and non-stationary time series analysis . The original purpose for the EMD was to find a decomposition which made it possible to use the instantaneous frequency for time-frequency analysis of non-stationary signals.

In this method we have found the totally adaptive signal decomposition we had been looking for in our image compression work, and we expanded the concept of EMD into two dimensions for image analysis and compression purposes.

Some implementations of the EMD in two dimensions generates a residue with many extrema points. In the papers below we present an improved method that can decompose the image into a number of IMFs and a residue with none, or with only a few extrema points. This method makes it possible to use the EMD for image processing. We introduce the concept of empiquency, short for empirical mode frequency, to describe the signal oscillations when traditional frequency concept is not applicable in this work. We also discuss the selection of significant extrema points as a tool for noise reduction.

Matlab code

Decompose an image into its intrinsic modes IMFs and corresponding residues. Download

NOTE:
The interpolation use 'tpaps' in the Matlab 6.5 Splines toolbox. This is extremely slow and memory consuming; Please make a better implementation and tell me about it.

This code may be used for education and inspiration. If using this code results in published work a reference to the source must be included in the paper:
http://go.to/imageemd

Link to code for one-dimensional analysis here

Selected Publications

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All articles/papers/reports with a logo are downloadable in the PDF format.

Conference Papers

A. Linderhed,
2D empirical mode decompositions in the spirit of image compression, Wavelet and Independent Component Analysis Applications IX , SPIE Proceedings Vol. 4738, April 2002, pp: 1-8.,
A. Linderhed,
Image compression based on empirical mode decomposition, Uppsala, March 11-12, 2004, Proc. of SSAB 04 symp. on image analysis, pp: 110-113.,
Corrected version
A. Linderhed,
Extrema Point Selection for Image Empirical Mode Decomposition, Malmö, March 10-11, 2005, Proceedings of Symposium on Image Analysis, SSAB’05, Malmö, Sweden, pp 133-136.
A. Linderhed,
Compression by Image Empirical Mode Decomposition, 2005. ICIP 2005. IEEE International Conference on Image Processing, Publication Date: 11-14 Sept. 2005, Volume: 1, On page(s): I- 553-6

Journal Articles

ANNA LINDERHED "IMAGE EMPIRICAL MODE DECOMPOSITION: A NEW TOOL FOR IMAGE PROCESSING", Advances in Adaptive Data Analysis (AADA) , 2009, Vol. 1, No. 2,

A. Linderhed, Variable Sampling of the Empirical Mode Decomposition of Two-Dimensional Signals, Special issue on "Sampling and Frames in Wavelet Theory and Time-Frequency Analysis" of the International Journal of Wavelets, Multiresolution and Information Processing. vol. 3, no. 3, pp. 435–452, 2005.
Preprint

Thesis

A. Linderhed,
Adaptive Image Compression with Wavelet Packets and Empirical Mode Decomposition, PhD thesis, Linköping University, Image Coding Group, 2004.
Download Thesis