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.

Date Published: 3 September 2009
PDF: 10 pages
Proc. SPIE 7446, Wavelets XIII, 74460O (3 September 2009); doi: 10.1117/12.825300

Published in SPIE Proceedings Vol. 7446:
Wavelets XIII
Vivek K. Goyal; Manos Papadakis; Dimitri Van De Ville, Editor(s)