The operations of digitization, transmission and storage of medical data, particularly images, require increasingly effective encoding methods not only in terms of compression ratio and flow of information but also in terms of visual quality. At first, there was DCT (discrete cosine transform) then DWT (discrete wavelet transform) and their associated standards in terms of coding and image compression. The 2nd-generation wavelets seeks to be positioned and confronted by the image and video coding methods currently used. It is in this context that we suggest a method combining bandelets and the SPIHT (set partitioning in hierarchical trees) algorithm. There are two main reasons for our approach: the first lies in the nature of the bandelet transform to take advantage of capturing the geometrical complexity of the image structure. The second reason is the suitability of encoding the bandelet coefficients by the SPIHT encoder. Quality measurements indicate that in some cases (for low bit rates) the performance of the proposed coding competes with the well-established ones (H.264 or MPEG4 AVC and H.265 or MPEG4 HEVC) and opens up new application prospects in the field of medical imaging.