In this thesis, a new structure for VQ, called as Tree-Structured Residual VQ (TSRVQ) with storage constraint, is proposed by modifying the ordinary TSVQ based on translation invariant property of VQ. The proposed scheme alleviates both computation and storage requirements, and is specially proper for image coding of large block size(8x8 or more). For the design of the TSRVQ with storage constraint, a simple codebook sharing technique is developed based on the direct measurement of the statistical similarity between different residual vector sources. Since the basic structure of the TSRVQ is same as the one of a tree structured VQ, it can be easily extended to the variable rate version by applying greedy tree growing algorithm with minor modification. In order to improving the performance of a memoryless TSRVQ, memory has to be incorporated. We applied the conventional predictive VQ scheme with a new linear vector predictor to the TSRVQ (Predictive TSRVQ (PTSRVQ)). Computer simulations for the proposed schemes have been performed for various test images and the results were compared with the ones from the conventional VQ schemes such as MSVQ. The results show that the proposed TSRVQ outperform the MSVQ over all range of bit rates with marginal storage increment and its variable rate version can achieve significant improvement in the rate-distortion performance compared with fixed rate coding. And as expected the PTSRVQ shows excellent performance in objective quality as well as subjective quality compared with JPEG and memoryless TSRVQ at a low bit rate range.