Stability Analysis of LASSO and Dantzig Selector via Constrained Minimal Singular Value of Gaussian Sensing Matrices
نویسنده
چکیده
In this paper, we introduce a new framework for interpreting the existing theoretical stability results of sparse signal recovery algorithms in practical terms. Our framework is built on the theory of constrained minimal singular values of Gaussian sensing matrices. Adopting our framework, we study the stability of two algorithms, namely LASSO and Dantzig selector. We demonstrate that for a given stability parameter (noise sensitivity), there exits a minimum undersampling ratio above which the recovery algorithms are guaranteed to be stable.
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