You recall that I mentioned on monday this paper on Signal Recovery on Incoherent Manifolds by Chinmay Hegde and Richard Baraniuk. Well, Chinmay Hegde just sent me the following about the statement on the RIP thingy ( I got some feedback from others offline as well :-)) Chin also makes available a prototype of the SPIN toolbox, woohoo !
Dear Igor,Thanks for the feedback, and for discussing SPIN on your most recent blog entry.Your comment on the blog about RIP and the theory/practice disconnect raises an important point.However, in the matrix decomposition problem, it seems that the issues are more subtle. Even with full measurements (i.e., \Phi = identity), it is unclear if a projected-gradient type algorithm can perfectly separate a matrix into its low-rank and sparse components. All current algorithms assume some sort of additional manifold structure (e.g., bounded singular vectors for the low-rank component; uniformly distributed nonzeros for the sparse component), but in those cases the projection operators become tricky to implement. Definitely food for thought..Regarding software: more work on SPIN is forthcoming, but for now I decided to release a small toolbox with code and test datasets that can reproduce the results in our IT submission.The software can be downloaded at http://dsp.rice.edu/software/spin-toolboxLastly: I really enjoy reading Nuit Blanche; it is an invaluable resource for our community. Thanks!-Chin
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