Abstract
As an extension of the widely used lr-minimization with 0 < r ≤ 1, a new non-convex weighted lr − l1 minimization method is proposed for compressive sensing. The theoretical recovery results bas ...
Highlights
Compressive sensing (CS) has attracted a great deal of interests since its advent [1, 2], see the monographs [3, 4] and the references therein for a comprehensive view
As an extension of the lr-minimization, we study in this paper the following weighted lr − l1 minimization problem for sparse signal recovery: min z∈RN
We evaluate the recovery performance by the signal to noise ratio (SNR), which is given by SNR = 20 log10
Summary
As an extension of the widely used lr-minimization with 0 < r ≤ 1, a new non-convex weighted lr − l1 minimization method is proposed for compressive sensing. The theoretical recovery results based on restricted isometry property and q-ratio constrained minimal singular values are established. An algorithm that integrates the iteratively reweighted least squares algorithm and the difference of convex functions algorithm is given to approximately solve this non-convex problem. Numerical experiments are presented to illustrate our results. Reviewed by: Junhong Lin, École Polytechnique Fédérale de Lausanne, Switzerland Richard G. Data Science, a section of the journal Frontiers in Applied Mathematics and Statistics
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