Moving forward from the recent Synthesis and L1 entries, I am trying to now review some of the new work on compressed sensing that do not generally fall into the traditional subjects of just compressive sampling.
- Lawrence Carin, Dehong Liu, Wenbin Lin, and Bin Guo, seem to be continuing on their interest in solving the Helmoltz equation with their new preprint: Compressive sensing for multi-static scattering analysis. (Preprint, 2007). It is important because we are beginning to see how their Bayesian Compressive Sensing software helps in solving an integral equation. I am sure I will come back to that paper once I see how it could be used. Right now only inverse problems come to my mind.
- Full Regularization Path for Sparse Principal Component Analysis by Alexandre d'Aspremont, Francis Bach, Laurent El Ghaoui. As far as I could tell the crux of their paper is to use the compressed sensing framework to sparsify the result of a PCA analysis. The generic problem with PCA is that most (few) Principal vectors of interest end up being full (not sparse). Their approach is to use the compressed sensing framework to find the Sparser Principal Components. Note, the code for the DSPCA (Sparse PCA using semidefinite programming) can be found here.
- I could not review this paper by Ashwin Wagadarikar, Renu John, Rebecca Willett, and David Brady. "Single disperser design for compressive, single-snapshot spectral imaging," SPIE Optics and Photonics, 2007. [http://www.ee.duke.edu/
~willett/papers/WagadarikarSPI] because the pdf file seems to be bad. E2007.pdf
- On a very local note, Ron DeVore will give a course on Compressed Sensing at Texas A&M University in the Math department this fall: Math 689 Section 602, in Blocker, http://www.math.tamu.edu
- If you know of a specific class or presentation made on the subject of Compressed Sensing and related areas please send me an e-mail, I'll try to make to map those and make it available.
- [Update: August 20. Muthu Muthukrishnan pointed to a variant of the JL transform by Jiri Matousek (here ). Does this new transformation follow the RIP ?]