The ℓ1 analysis approach by sparse dual frames for sparse signal recovery represented by frames

A sparse-dual-frame based ℓ₁-analysis approach for compressed sensing (CS) is proposed. The sparse dual frame is a notion of optimal dual frames of a non-exact frame. It is motivated in the study of compressed sensing problems where signals are sparse with respect to redundant dictionaries (frames). An alternating iterative algorithm is proposed. An error bound ensuring the correct signal recovery is obtained. Empirical studies over generally difficult CS problems demonstrate that the new sparse-dual-based approach provides satisfactory solutions, whereas other existing means may not.