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construct a Basis function to represent a sparse signal

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Sherra

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Hi all,

Does anyone know how to construct a basis function (Fourier, Bayesian, wavelet function, generalized basis function...) in matlab to represent a sparse signal. The problem is I have a signal in time domain, I know it is sparse in some basis, but how to find that basis? The problem could be reformulated as as : knowing h (1000,1) in some conventional basis, I am looking for the matrix "Phi" such that , < h=Phi*h_sparse >.
h_sparse is the same as h, only represented in another basis and having lots of zeros entries.
Thanks for any help!!!
 

I wanted to add something to make myself clear enough. How do I choose a dictionary (overcomplete basis) in which to represent a signal, that is in time domain, to get its sparse representation?

thank you!!
 

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