Hierarchical encoding, initially developed for image decomposition, is a feasible alternative for image transmission and storage. Several independent compression strategies can be implemented, and, therefore, applied at the same time. Lossless encoding o Universal statistical compression on the hierarchical code. A unique Huffman code, valid for every hierarchical transform is built. Lossy encoding o Improvement of the intermediate approximations, as this can decrease the effective bit rate for transmission applications. Interpolating schemes and non-uniform spatial out-growth help solve this problem. o Prediction strategies on the hierarchical code. A three-dimensional predictor (space and hierarchy) on the code-pyramid reduces the information required to build new layers. o Early branch ending. Analysis of image homogeneities detects areas of similar values that can be approximated by a unique value.