March 22, 2008

Compressive sensing - Processing Vein Mess

This first short note on Compressive Sensing is, of course, anagram-driven since it has been applied for some Vein Mess Processing (see the images on the last page of Sparse MRI: The Application of Compressed Sensing for Rapid MR Imaging, by Michael Lustig, David Donoho and John M. Pauly). Some matlab code for compressed sensing MRI is made available. It is also dedicated to Igor Carron who carefully blogs and extracts information bits from the overwhelming litterature on CS (see Compressive Sensing Resources). For short, compressed or compressive sensing aims at saving bits by sampling and compressing structured signals at the same time, allowing some potential error. It is strongly related to sparse decompositions. An open challenge: find the sparsest/most compressed, but also most elegant, definition for "compressive sensing"! I do consider the four-word Wedderburn theorem "every finite field commutates" (in French: "tout corps fini commute", with open poetic interpretations) one of the beautiful mantras (sure, allowing an amount of metonymia, five-word versions are more correct). The right-side image of a "corps fini" is borrowed from here.
It is also meant to provide recordings from talks around the topic, for the unfortunate who could not attend. Most of the talks rest of the wonderful Diffusion des savoirs de l'Ecole Normale Supérieure site, especially for the Mathematical Foundations of Learning Theory conference.

Compressive sensing may solve some problems. Hope it could also contribute to stock exchange troubles by improving SEC Senses. While standard banks fail, filter banks (and wavelets of course) never deceive.