Sparse Recovery Problem Solution

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S. David 2014-6-27

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https://ww2.mathworks.cn/matlabcentral/answers/138011-sparse-recovery-problem-solution

评论： S. David 2014-6-30

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