Аннотация:
In this paper, we study the recovery conditions of weighted $\ell_{1}$ and $\ell_{1-2}$-minimization for signal reconstruction from compressed sensing measurements when multiple support estimate sets with different accuracy are available. First, we consider the recovery condition of signals with additive $\ell_{2}$ noise via $\ell_{1}$-minimization in the framework of cumulative coherence when arbitrarily many distinct weights are permitted. We also change this condition in the framework of mutual coherence. Second, we consider the recovery condition of signals with additive $\ell_{2}$ noise via $\ell_{1-2}$-minimization in the framework of mutual coherence when arbitrarily many distinct weights are permitted.
Ключевые слова:
signal reconstruction, weighted minimization, weighting set.
