Tuesday, May 22, 2012

The answer is still No

I don't get personal when it comes to spam, except for today:'s batch :)

.....The very next time I read a blog, I hope that it doesn't disappoint me just as much as this particular one. I mean, I know it was my choice to read, however I actually thought you'd have something helpful to say. All I hear is a bunch of whining about something that you could fix if you were not too busy looking for attention.....
It wasn't really a question, rather a comment but my answer is No

In the meantime, I answered a question on Compressed Sensing applicability on the new dsp stackexchange. Of interest is an item I never mentioned out loud before: Imagine you have a non sparse signal and then add zeros to make it sparse and then use compressed sensing to sample that signal, wouldn't it better than directly sampling the full signal? 

The answer is still No.

It turns out that the bounds for which CS work would eventually be less efficient than just performing a full sampling of the original (full/non-zero) signal. In other words, the number of CS measurements required would be higher than the number of non-zero elements in the signals. By sparsifying the signal, you are "losing" on purpose the information about where the signal is supported (i.e. non-zero). The hard part of Compressive Sensing and attendant reconstruction solvers is to get that information back i.e. find the location of those non zero elements of the signal: If you know beforehand the locations of those non zero elements, then there is no need to go to a less efficient method of sampling that signal.
Finding the location of the non-zero elements of a signal is the reason we talk about NP-Hard, BPP and so forth...., up until 2004, we thought it was hard to do.

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