Multiple description coding using overcomplete linear expansions

Multiple Description (MD) coding is the coding of a source into multiple descriptions so that any arbitrary subset of the descriptions gives an estimate of the source that is commensurate with the rate of the subset of descriptions. The recent interest in multiple description coding has arisen from the application of such coding algorithms to code a source for transmission over an erasure channel, such as a packet loss network. These techniques are an alternative to traditional coding schemes of first performing lossy compression on data followed by error protection schemes for reliable transmission. One of the main practical MD coding algorithms has been the use of overcomplete linear expansions, which are also known as frame expansions. Topics of interest to MD coding using overcomplete linear expansions are studied in this thesis. An efficient algorithm for obtaining consistent reconstructions is developed for the case in which the expansion can be written as a concatenation of a few orthonormal transforms. Also presented are algorithms to optimize the transform and bit allocation when channel characteristics are known. Finally, overcomplete expansions are extended from simple block transforms to subband expansions. Optimization of overcomplete subband expansions is also presented.