On the Null Space Constant for Minimization
نویسنده
چکیده
The literature on sparse recovery often adopts the “norm” ( ) as the penalty to induce sparsity of the signal satisfying an underdetermined linear system. The performance of the corresponding minimization problem can be characterized by its null space constant. In spite of the NP-hardness of computing the constant, its properties can still help in illustrating the performance of minimization. In this letter, we show the strict increase of the null space constant in the sparsity level and its continuity in the exponent . We also indicate that the constant is strictly increasing in with probability 1 when the sensing matrix is randomly generated. Finally, we show how these properties can help in demonstrating the performance of minimization, mainly in the relationship between the the exponent and the sparsity level .
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