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This paper discusses a fundamental problem in compressed sensing: the sparserecoverability of L1 minimization with an arbitrary sensing matrix. We developan new accumulative score function (ASF) to provide a lower bound for therecoverable sparsity level (SL) of a sensing matrix while preserving a lowcomputational complexity. We first define a score function for each row of amatrix, and then ASF sums up large scores until the total score reaches 0.5.Interestingly, the number of involved rows in the summation is a reliable lowerbound of SL. It is further proved that ASF provides a sharper bound for SL thancoherence We also investigate the underlying relationship between the new ASFand the classical RIC and achieve a RIC-based bound for SL.

New Accumulative Score Function Based Bound For Sparsity Level of L1 Minimization