Constructions of dual frames compensating for erasures with implementation

Let I N be a finite or infinite set and let (xₙ) ₍ ₈ be a frame for a separable Hilbert space H. Consider transmission of a signal h where a finite subset (h, xₙ) ₍ ₄ of the frame coefficients (h, xₙ) ₍ ₈ 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) ₍ ₈ ₄ which is then used for perfect reconstruction from the preserved frame coefficients (h, xₙ) ₍ ₈ ₄. There are several methods for such construction, starting from the canonical dual or any other dual frame of (xₙ) ₍ ₈. We implemented the algorithms for these methods and performed tests to compare their computational efficiency.