Tuesday, October 08, 2013

Compressed Counting Meets Compressed Sensing

So streaming measurements are coming to compressive sensing.  The idea is that what is being measured is only seen once. 

From the paper, I note that, if I understand correctly, the measurement matrices is a lower diagonal one and every column is the identity multiplied by a scalar. That is one strange measurement matrix. 

Compressed sensing (sparse signal recovery) has been a popular and important research topic in recent years. By observing that natural signals are often nonnegative, we propose a new framework for nonnegative signal recovery using Compressed Counting (CC). CC is a technique built on maximally-skewed p-stable random projections originally developed for data stream computations. Our recovery procedure is computationally very efficient in that it requires only one linear scan of the coordinates. Our analysis demonstrates that, when 0
0 and C=pi/2 when p=0.5. In particular, when p->0 the required number of measurements is essentially M=K\log N, where K is the number of nonzero coordinates of the signal.

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