A variant of the S-transform (ST), which is a multiresolution Walsh-Hadamard transform having the structure of a dyadic wavelet decomposition, is proposed for both speeding up computation,and enabling extension to 3D data, when reversible coding of medical images and image sequences is concerned. It is derived by exploiting the same parity of the sum and the difference of two integers in a separable fashion, and thereby it has been easily extended to decorrelate volumetric data. Also, the spatial structure of the ST is considered by modelling the statistics of the different subbands of integer coefficients as generalized Gaussian probability density functions (PDF), and by fitting individual codebooks for variable length coding. The estimate of the shape factor of the PDF is based on a novel criterion matching the entropy of the theoretical and actual distributions. Coding performance comparisons are made with a similar algorithm, like the reduced-difference pyramid (RDP), designed for the purpose of hierarchical lossless image compression,as well as with lossless JPEG. Tests carried out on medical images and tomographic sequences show improvements of the proposed scheme over both the RDP and the 2D ST. Archival/retrieval are feasible on-line, still with the benefits of multiresolution coding for telebrowsing.