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I am newbie in compressive sensing (CS), I read about compressive sensing and its use for sparse vector estimation. As I understood CS can be used either in time or frequency domain. For me, The part I couldn't understand in my case is how to build the measurement matrix for my vector required to be estimated. (In my case the sparse vector $h$ needs to be estimated)

I have a vector $X$ where some values of it are known (let's say the values located at $1:4:end$), called pilots, that vector was convoluted with a sparse vector $h$, to have:

$y = X*h$

$*$ denotes the convolution operation.

My goal is to estimate the sparse vector $h$ based on the known values (pilots) in $X$. How to build the measurement matrix in that case?

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    $\begingroup$ In order to be able to use CS, it's better to change the convolution into multiplication, such that $y= X*h = XH$ where $H$ is the toeplitz matrix of h, but I don't know how to deal with your measurement matrix exactly. $\endgroup$ Jun 27 '20 at 2:43
  • $\begingroup$ Ok. I think we can write one of them since they are the same $\endgroup$
    – Fatima_Ali
    Jun 27 '20 at 11:01
  • $\begingroup$ I don't know if that means it's not possible to use compressive sensing in that case or my question was n't read by someones who know about the compressive sensing. $\endgroup$
    – Fatima_Ali
    Jun 29 '20 at 2:53
  • $\begingroup$ I think it's difficult to use CS in your case, but I'm not sure! $\endgroup$ Jul 3 '20 at 11:52

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