Assume I have a sparse vector $$x$$ whose few values are non-zeros, that vector is multiplied with sparse unitary matrix $$Y$$ giving $$z = Yx$$. Are there any advantages of detecting the sparse vector $$x$$ based on $$z$$ the in that case?

• I don't understand the question. "detection of $x$" requires that you have something that you're not sure contains $x$ or doesn't contain $x$. What is that? (context is key!) – Marcus Müller Jun 5 '20 at 18:04