Subband filters optimized for lost coefficient reconstruction

Packet-based transmission of subband coded images over lossy networks presents a reconstruction problem at the decoder. Accurate reconstruction of the high-energy low frequency subband coefficients is imperative in providing consumer-grade image quality. This paper introduces a family of one-dimensional quadrature mirror filters (QMFs) designed to minimize the mean-squared error of reconstructed low frequency coefficients for a given reconstruction algorithm to be implemented at the decoder. Mean-reconstruction, in which a missing coefficient is replaced with the average of its neighbors either horizontally or vertically, is selected for its simplicity and implementation ease. The resulting filters perform well as QMFs and provide the desired reconstruction properties in the event of loss. While the filters are developed using mean-reconstruction the filter design algorithm can be used with more sophisticated reconstruction techniques, providing that the mean-squared error can be expressed in the appropriate quadratic form.