Wavelet and tree-structured filter bank based coding schemes find application in a number of image coding algorithms. The efficiency of such coding schemes can be enhanced further by adapting the parameters of the coder to the statistics of the signal being compressed. In this paper, we propose an algorithm to determine the coefficients of the filter bank matched to the signal statistics, at every node of a tree-structured filter bank. In the proposed algorithm, we visit each node in a top-down fashion and determine the bit- allocation and the coefficients of the filters used to carry out the decomposition. An estimate of the coding gain provided by the later stages is used to account for the interaction between the filter bank at the current node and the filter banks at the later nodes.