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\label{fig:NumericsResults} Percent of entries that must be sampled for accurate recovery(\(< 10^{-7}\) relative error)  of a matrix, matrix  as a function of sparsity. Comparison between compressed sensing and two limiting cases: ``no prior knowledge'' of sparsity and the ``perfect oracle'' who reveals where all non-zero entries are located. Each point on the compressed sensing curve is an average of ten different randomizations. The acuracy criterion is a relative error in the Frobenius norm smaller than \(10^{-7}\).