## Sunday, October 30, 2011

### Hanging out on Compressive Sensing

Muthu had a hangout session last week on compressive sensing but for technical reasons I simply could not connect correctly to that session. I think Hangout as a product has a long way to go before I would recommend it to anybody. In the meantime, Muthu listed some of the subjects mentioned then:

• 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: 12, ..

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