Sunday, October 30, 2011

Video hangout with the World: Update

Last week was the first experiment with two hosts focused on a topic. The topic was Compressed Sensing (CS), and the main host was Igor Carron. There were 10+ people trying to get on the call at various times and not all could get on. Igor was in and out due to technical problems. Bottomline: our technique for video hangout with the world will keep improving, and we need another session later where Igor will have a platform to address the many issues that come up, with his encyclopedic insights into CS.

Last week, we talked about:
  • Functional CS. Minimize number of measurements needed to not reconstruct the signal, but estimate various functions of the signal. Streaming algorithms can be seen to be in this genre, but they dont provide the typical for-all signals guarantee or provide insights on what is a suitable notion of class of all ``compressible'' signals for a function of interest. Eric Tramel who was in the call and has image analysis background, proposed ``smoothness'' or total variation distance as a function to estimate. Defined as \sum_i (A[i]-A[i-1])^2, this does not seem to be a new problem: it is L_2 norm squared, and inner product. But some variation of this may be of interest. Some old thoughts on functional CS is here.
  • Linear measurements are the key to compressed sensing. What is the status on building hardware that will do linear measurements from analog signals that is faster/more efficiently than standard Nyquist sampling?
  • What is the status of CS for arbitrary dictionaries (not necessarily, orthonormal). Did any new algorithmic technique beyond usual pursuit + group testing algorithms get developed?
  • What are the latest developments in CS for matrix approximation?
  • What are recent CS conferences? Examples: 1, 2, ..



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