Recovery of Transmission Losses by Optimal Linear Filtering in a Multiresolution Image Transmission Scheme

In this paper, we are trying to recover coefficients lost during the transmission of subband-encoded images. Unlike many authors in the field of image reconstruction, we are dealing with coefficient losses (represented by a given loss probability) and not with additive noise or propagation effects modeled by a particular transmission function. Our channel can be considered as a digital packettransmission system, where a given percentage of the packets do not reach the receiver. We also assume that the lost coefficients can be determined, e.g. thanks to a labeling of the packets. We are using linear filters in order to predict those missing coefficients from their neighbours. This paper deals with the design of optimal filters based on the available data. This goal is achieved by solving the classical Yule–Walker equations. However, due to the lossy structure of the data, several problems arise, mainly related to the estimation of the correlation matrices used in those equations. Different schemes have been experimented, in order to achieve the best reconstruction without excessively expensive computations. We have tried different correlation estimators and different sets of neighbours used to recover the missing points. The simulation results show that our filters provide good reconstruction performances, both visually and in terms of a PSNR, with respect to the classical median filter. They are also quite insensitive to the choice of various parameters and they do not need any side information, as the filters are 1This author would like to thank the Belgian National Fund for Scientific Research (FNRS) for its financial support. optimised by using only the received data.