Sparse Recovery Problem Solution

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S. David
S. David on 27 Jun 2014
Commented: S. David on 30 Jun 2014
Hello all,
I am working on a communication system where I physically have Np triplets {hp,taup,ap}. From these Np triplets I can build the exact channel matrix.
In practice however I need to estimate the channel. To estimate the channel I first build the dictionaries tau of cardinality Nt and a of cardinality Na. From these dictionaries I form the equation Ax=z, where z is the noisy observation vector, A=[Gamma1*Lambda1*s ... Gamma1*LambdaNt*s .... GammaNa*Lambda1*s .... GammaNa*LambdaNt*s] and x=[x(1,1) ...x(1,Nt) .... x(Na,Nt)]=[x1 ... x_NaNt]. s is the known pilot symbols.
Obviously, x is sparse, and I am using the Basis Pursuit (BP) algorithm to find it. The problem is that when solving the problem x contains much more that Np non-zero elements. How can I find Np unique triplets from Ax=z? This means there is no two triplets share the same hp, taup or ap?
Thanks
  9 Comments
S. David
S. David on 30 Jun 2014
Thanks for explanation.
Indeed, just one entry, which is the first entry of the solution, is 1 and the rest are zeros.

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