A low complexity replacement scheme for erased frame coefficients

Bernhard G. Bodmann; Peter G. Casazza; Gitta Kutyniok; Steven Senger

doi:10.1117/12.825300

3 September 2009 A low complexity replacement scheme for erased frame coefficients

Bernhard G. Bodmann, Peter G. Casazza, Gitta Kutyniok, Steven Senger

Proceedings Volume 7446, Wavelets XIII; 74460O (2009) https://doi.org/10.1117/12.825300
Event: SPIE Optical Engineering + Applications, 2009, San Diego, California, United States

Abstract

One key property of frames is their resilience against erasures due to the possibility of generating stable, yet over-complete expansions. Blind reconstruction is one common methodology to reconstruct a signal when frame coefficients have been erased. In this paper we introduce several novel low complexity replacement schemes which can be applied to the set of faulty frame coefficients before blind reconstruction is performed, thus serving as a preconditioning of the received set of frame coefficients. One main idea is that frame coefficients associated with frame vectors close to the one erased should have approximately the same value as the lost one. It is shown that injecting such low complexity replacement schemes into blind reconstruction significantly reduce the worst-case reconstruction error. We then apply our results to the circle frames. If we allow linear combinations of different neighboring coefficients for the reconstruction of missing coefficients, we can even obtain perfect reconstruction for the circle frames under certain weak conditions on the set of erasures.

Citation Download Citation

Bernhard G. Bodmann, Peter G. Casazza, Gitta Kutyniok, and Steven Senger "A low complexity replacement scheme for erased frame coefficients", Proc. SPIE 7446, Wavelets XIII, 74460O (3 September 2009); https://doi.org/10.1117/12.825300

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