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M \propto \mu^2 S \log N^2\ .  \end{equation}  %  This scaling equation encapsulates the important aspect of compressed sensing: if a proper measurement basis is chosen, the number of entries which must be measured scales linearly with the sparsity of the matrix and only depends weakly on the full size of the matrix. For the remainder of this paper, we always choose our measurement basis vectors to be the discrete cosine transform (DCT) of the sparse basis vectors, whose parameter \(\mu\) isequal to  \(\sqrt{2}\). In order to study the numerical properties of the reconstruction method we performed a series of numerical experiments. We generate \(100 \times 100\) matrices of varying sparsity with random values drawn uniformly from the interval \([-1,1]\) and places in random locations in the matrix. Matrix elements were then sampled in the DCT measurement basis, and an attempt was made to recover the original sparse matrix by solving the compressed sensing basis pursuit problem in eq.~\ref{eq:bpdn}.