CS: Insight in Performance limits for jointly sparse signals via graphical models.

Here is some additional inisight on the paper entitled Performance limits for jointly sparse signals via graphical models by Marco Duarte, Shriram Sarvotham, Dror Baron, Michael Wakin , and Richard Baraniuk. I have covered it here and here before, but the poster is new.

Furthermore, Dror Baron who is currently doing compressed sensing in Israel wanted to point out the following insight that will hopefully push more people into thinking of CS as a way of implementing distributed systems:

The interesting point is that in the world of noiseless measurement of strictly sparse signals, dimensionality plays a volumetric role analogous to entropy in the data compression world. We have shown a generic bound that applies in the following settings:

1. Single signal CS: one signal being measured noiselessly.
2. Joint CS: one encoder looks at an ensemble of signals and measures them jointly (together), the CS measurements are multiplication of a matrix by the vector of the entire ensemble. Not surprisingly, the bounds here are similar to single signal CS.
3. Distributed CS: again there are multiple signals, but here they are measured in a distributed manner, and each is encoded (measured) differently by a different measurement matrix. We provide a region describing the number of noiseless measurements required for each of the the signals. Surprisingly, the sum of the number of measurements is very similar to before.

In my view, the real contribution here is that in the idealized world of noiseless strictly sparse signals, the dimensionality of the signal ensemble under evaluation provides a precise characterization of the number of measurements required. This really enhances and magnifies the role that dimensionality plays in these systems. Although this is perhaps an idealized application, it can provide insights into noisy measurement systems, which is of interest to me.