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Optimal frames have been used in signal processing to minimize the reconstruction errors when erasures occurred during the frame coefficient transmission, and much of the recent work has been focused either on characterizations or on the constructions of optimal frames (or dual frames) prior to signal encoding. In this paper, we propose a new approach, based on the method of optimal directions, which can search adaptively optimal dual frames in the process of signal reconstruction. We provide concrete algorithms for constructing adaptive optimal dual frames and the reconstruction of signals. In addition, several numerical experiments are presented to demonstrate the efficiency and comparison of the new method with the existed methods.

Adaptive Optimal Dual Frames for Signal Reconstruction With Erasures