Recovery of High-Dimensional Sparse Signals via ℓ1-Minimization

Abstract EN

We consider the recovery of high-dimensional sparse signals via ℓ1-minimization under mutual incoherence condition, which is shown to be sufficient for sparse signals recovery in the noiseless and noise cases.

We study both ℓ1-minimization under the ℓ2 constraint and the Dantzig selector.

Using the two ℓ1-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.