This project investigates how signals can be accurately reconstructed when some transmitted measurements are lost. Frame theory provides a mathematical framework for representing signals with redundancy, allowing recovery even when certain frame coefficients are erased. We study a reconstruction method called bridging, which estimates missing frame coefficients by approximating the corresponding frame vectors using combinations of the remaining vectors. Two strategies for selecting these vectors are considered: NormCut, which selects vectors based on distance, and AngleCut, which selects vectors based on directional alignment in the Hilbert space. Numerical experiments analyze how reconstruction accuracy depends on frame redundancy, the number of erased coefficients, and the number of vectors used in the approximation. The results show that both bridging methods significantly improve reconstruction compared to partial recovery, with the AngleCut method consistently producing the lowest reconstruction error.
