In this thesis work, three problems for the improvement of conventional transform coders are investigated. By an accurate representation of the parametric distortion function in the block quantization, new normalized variance levels for bit allocation are obtained. It has been shown that the performance of the new scheme is about 15-25 percent better than that of a conventional one. In the adaptive two-dimensional transform coding with activity classification, several classification measures are investigated in view of adaptation and hardware simplicity. It has been found that the partial sum of the absolute coefficient values of the first quarter, scanned by a zig-zag pattern in each transformed block, is the most efficient measure. Lastly, for a direct processing without a large amount of buffer, the firstorder Markov modelling is investigated. It has been found that it can be suitably used in the one-dimensional transform coding, but not in the two-dimensional transform coding. In addition, the recursive algorithm for a direct processing in the two-dimensional transform coding and two types of hybrid coding, transform-DPCM and DPCM-transform, have been studied. Simulations have been made with two 8-bit resolution 256x256 size images called GIRL and COUPLE and the reconstructed images are taken from a displayer of 4-bit resolution for 128x128 size, after averaging the adjacent four pixels.