Spectrum-based decomposition of a 2D input signal into k band-separated modes. Here, we propose an entirely non-recursive variational mode decomposition model, where the modes are extracted concurrently. The model looks for an ensemble of modes and their respective center frequencies, such that the modes collectively reproduce the (2D) input signal, while each being smooth after demodulation into baseband. The variational model is efficiently optimized using an alternating direction method of multipliers approach.
This is a generalization of 1D VMD:
http://www.mathworks.com/matlabcentral/fileexchange/44765-variational-mode-decomposition
See: K. Dragomiretskiy and D. Zosso, Variational Mode Decomposition, IEEE Trans. Signal Processing 62(3):531-544, 2014. http://dx.doi.org/10.1109/TSP.2013.2288675

and

K. Dragomiretskiy and D. Zosso, Two-Dimensional Variational Mode Decomposition, IEEE Int. Conf. Image Proc. 2014, (submitted). Preprint: ftp://ftp.math.ucla.edu/pub/camreport/cam14-16.pdf