A para-pseudo inverse based method for reconstruction of filter bank frame-expanded signals from erasures

Packet losses due to congestion or buffer overflows is a common problem in packet switched networks. Current network protocols manage this problem by retransmitting the lost packets. However, the delay due to the retransmission of the lost packets may be unacceptable for many real-time applications. Recent focus to resolve this problem is to recover the lost data from the received packets using some error control coding scheme. In this context, signal representation using frames has gained attention and has been studied in J. Kovacevic et al. (2002), P.L. Dragotti et al. (2001), G. Rath and C. Guillemot (2004), and R. Motwani and C. Guillemot (2004). Oversampled transforms and oversampled filter banks have been considered as joint-source channel codes and methods for reconstructing from erasures is studied in these articles. However, for oversampled filter banks, the reconstruction methods based on operating the pseudo-inverse based on the entire signal length are computationally complex and those based on reconstructing the erasures are not optimal as far as reconstruction mean square error is concerned. In this paper, we propose a method for reconstruction from erasures using a synthesis filter bank which functions as a pseudo-inverse. Hence, the scheme minimizes the reconstruction mean square error. Further, the method is computationally efficient, because it does not operate the pseudo-inverse corresponding to the entire signal vector. The synthesis filter bank, which obviously depends on the erasure pattern implements the pseudo-inverse at a practical computational cost. Some typical bursty erasure patterns which permit existence of a FIR synthesis filter banks are studied. The theoretical results are validated for bursty erasure patterns by simulations using image data.