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The size of the set \(W\), a number that we call \(M\), is the number of matrix elements of \(B\) that we need to sample and it determines the quality of the reconstruction of \(A\). From compressed sensing theory we can find a lower bound for \(M\), as a function of \(P\), \(S\) and \(N\).  One important requirement for compressed sensing is that the basis \(\{\psi_i\}\) for \(A\) and the basis \(\{\phi_i\}\) for \(B\) should be \textit{incoherent}, meaning that the maximum overlap between any vector inthe  \(\{\psi_i\}\) and \(\{\psi_i\}\) any vector in \(\{\phi_i\}\)  \begin{equation}  \label{eq:coherence}  \mu = \sqrt{N} \max_{i,j} \langle \psi_i | \phi_j \rangle