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different basis.  Suppose we wish to recover an \(N \times N\) matrix \(A\) known to be sparse in a particular orthonormal basis $\{\psi_i\}$(for simplicity we restrict ourselves to square matrices an orthonormal bases). Without no prior knowledge of where the \(S\) non-zero  entries of \(A\) are located, to recover the matrix we need to calculate all $\{\phi_i\}$. the elements of of the matrix.  \(\{\phi_i\}\).  The matrices \(A\) and \(B\) are related according to the change-of-basis formula  \begin{align}  \label{eq:cob_matrix}