Saturday, March 03, 2007

Smashed filters and Bayesian approach to Compressed Sensing among others

Found in the fantastic Compressed Sensing Resource at Rice. In terms of application, two fascinating papers just surfaced:

* The smashed filter for compressive classification and target recognition by Mark Davenport, Marco Duarte, Michael Wakin, Jason Laska, Dharmpal Takhar, Kevin Kelly, and Richard Baraniuk it is an extension of the Matched Filter theory to compressed measurements. The interesting part is that the ability to do classification is based in part on the dimension of the underlying manifold (generally it is low).

* Bayesian compressive sensing by Shihao Ji, Ya Xue, and Lawrence Carin, where there is description of a reconstruction scheme that relies on Bayesian inversion. The difference between this scheme and others is the ability to figure out how your convergence is doing during the signal reconstruction computations.

* Sparse MRI: The application of compressed sensing for rapid MR imaging.
Michael Lustig, David Donoho, and John M. Pauly, where compressed measurements are directly taken by "randomly" undersampling in the k-fourier space thereby enabling substantial savings in acquisition time.

* and the ever fascinating paper on The Johnson-Lindenstrauss Lemma Meets Compressed Sensing by Richard Baraniuk, Mark Davenport, Ronald DeVore, and Michael Wakin.

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