The goal of this research is to develop improved quantization and encoding methods, with direct application to image and video coding. The three main topics of study are i) exploiting interband dependence in subband coding, ii) joint source/channel coding with applications to image and video transmission over networks, and iii) lossy coding of motion vectors in video coding. Advanced image and video coding methods will be developed to quantize and encode across subbands, with the goal of providing granular gain, classification gain, and entropy gain. Joint source/channel image and video coding methods will be developed for wireless and packet-switched network applications, with the goal of providing graceful image degradation as the channel bit error rate or the network packet loss rate become large. Methods will be developed for the lossy encoding of the motion compensation vectors used in video coding, with the goal of determining a theory and practical algorithms for the optimum joint lossy coding of the motion compensation vectors and the prediction error.