Morphological Diversity using Sparse Constraints

Jerome Bobin just announced the opening of a site featuring most of his work and attendant Matlab code relevant to Morphological Diversity which is introduced as:

Recent advances in harmonic analysis and signal processing have advocated the use of overcomplete signal representations. The ability of such redundant signal dictionary to lead to very sparse representations has already been used successfully in various fields. In this context, morphological diversity has emerged as an effective signal analysis tool. The gist of morphological diversity consists in modeling signals as the linear combination of several so-called morphological components...

Recovering the morphological components from their combination then relies on the incoherence (morphological diversity) of their respective sparse representation (the DCT and Curvelet tight frame). Morphological Component Analysis (MCA) has been devised to solve this harsh recovery problem.

In the general case, a wide range of signal representations can be accounted for such as wavelets, contourlets, bandlets, wave atoms or curvelets.

Morphological diversity and Morphological Component Analysis (MCA) then turns to be a privileged tool for sparse signal representation.

This website has be designed so as to give a wide review of morphological diversity ‘s ability. This particular and effective framework has already been extended and applied to a very large range of applications in signal and image processing from texture/contour separation to source separation or compressed sensing. We really think that morphological diversity has just begun a fruitful and long life in signal processing.

The hyperspectral part of the website mentions the use of Mars Data and the upcoming availability of a code that does Blind Source Separation using Spatial and Spectral Sparsity Constraints. On a related note, ESA now provides access to Earth hyperspectral data from MERIS and Proba.

Credit Photo: ESA/DLR/FU Berlin (G. Neukum), Hyperspectral photo of Phobos, one of Mars' Moon taken by the Mars Express probe three years ago.