In the Generalized MCA (GMCA) framework, the sources  Each observation is the linear combination of original sources which are sparse in different basis. In these examples, the sources are assumed to be different spectrally (different mixtures) and morphologically (the sources are assumed to be sparsely represented in incoherent bases).

A first example : curves + cloud + noise

The original sources (left). Gaussian noise is added to each mixture (SNR = 6dB). The MMCA estimates (right) were computed from two mixtures (middle).

A second example : Boy + Texture + Noise

The original sources (left). Gaussian noise is added to each mixture (SNR = 14dB). The MMCA estimates (right) were computed from ten random mixtures (two of them are depicted in middle of the figure).

In theoe example, the redundant dictionary we used is composed of the union of Curvelets and DCT.

References :

1. ❖J. Bobin, Y. Moudden, J.-L. Starck and M. Elad, "Morphological Diversity and Source Separation", IEEE Signal Processing Letters, Vol.13, N°7, p. 409-412, July 2006.
   

2. ❖J. Bobin, Y. Moudden, J.-L. Starck, "Enhanced Source Separation by Morphological Component Analysis", IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2006), May 2006.
   

3. ❖J. Bobin, Y. Moudden, J.-L. Starck and M. Elad, "Multichannel Morphological Component Analysis", Proceedings of SPARS'05, November 2005.
   

4. ❖J.-L. Starck, Y. Moudden, J. Bobin, M. Elad, and D.L. Donoho, "Morphological Component Analysis", Proceedings of the SPIE conference wavelets, Vol. 5914, July 2005.

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