Reconstruction-optimized lapped orthogonal transforms

Packetized image communication over lossy channels presents a reconstruction problem at the decoder. To date, reconstruction algorithms have been developed for fixed coding techniques. This paper examines the dual problem — a block-based coding technique, namely a family of lapped orthogonal transforms (LOTs), is designed to maximize the reconstruction performance of a fixed reconstruction algorithm. Mean-reconstruction, in which missing coefficient blocks are replaced with averages of their available neighbors, is selected for simplicity and implementation ease. A reconstruction criterion is defined in terms of mean-squared error, and is used to define the reconstruction gain . A family of LOTs is then designed to consider both reconstruction gain and coding gain. Reconstruction capability and compression are exchanged, and the LOT family consists of transforms that provide increasing reconstruction capability with lower coding gain. A transform can therefore be selected based on channel loss characteristics, desired reconstruction performance, and desired compression.