A few graphs before I leave

Coming up next week: my seven consecutive lectures and workshops in artificial intelligence programming! In the meantime, I leave you with the following. Both of the graphs below represent recovery results of sparse signals from compressive measurements. The first uses sparse signals from the constant-amplitude random signs ensemble; the second uses sparse signals with non-zero elements distribute Normal. We see quite a difference between the two cases, as several of my previous experiments have shown, as well as the work by many others. However, I do not feel confident claiming that COLS (cyclic OLS) performs the best of those algorithms tested because once we no longer have perfect recovery, “best” becomes “least worst”. Still, when I look at the mean \(\ell_2\) and \(\ell_\infty\) norms of the latter simulations, COLS has the smallest values of all.

RecoveryProbabilityCARS.jpg
RecoveryProbabilityNormal.jpg
I was hoping to write up some of these results to submit to EUSIPCO 2011, but before I do I want to at least do a proper analysis of these cyclic algorithms, and involve some theoretical work in successive interference cancellation. Perhaps SPARS 2011…

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