Constructions of dual frames compensating for erasures with implementation

Let I⊆ N be a finite or infinite set and let (xₙ)n∈ I be a frame for a separable Hilbert space H. Consider transmission of a signal h where a finite subset ( h,xₙ)n∈ E of the frame coefficients ( h,xₙ)n∈ I is lost. There are several approaches in the literature aiming recovery of h. In this paper we focus on the approach based on construction of a dual frame of the reduced frame (xₙ)n∈ I E which is then used for perfect reconstruction from the preserved frame coefficients ( h,xₙ)n∈ I E. There are several methods for such construction, starting from the canonical dual or any other dual frame of (xₙ)n∈ I. We implemented the algorithms for these methods and performed tests to compare their computational efficiency.