Recovery of High-Dimensional Sparse Signals viaℓ1-Minimization

[摘要] We consider the recovery of high-dimensional sparse signals viaℓ1-minimization under mutual incoherence condition, which is shown to be sufficient for sparse signals recovery in the noiseless and noise cases. We study bothℓ1-minimization under theℓ2constraint and the Dantzig selector. Using the twoℓ1-minimization methods and a technical inequality, some results are obtained. They improve the results of the error bounds in the literature and are extended to the general case of reconstructing an arbitrary signal.

[学科分类] 应用数学