In the field of medical diagnostics, interested parties have resorted increasingly to medical imaging. It is well established that the accuracy and completeness of diagnosis are initially connected with the image quality, but the quality of the image is itself dependent on a number of factors including primarily the processing that an image must undergo to enhance its quality. This paper introduces an algorithm for medical image compression based on the quincunx wavelets coupled with SPIHT coding algorithm, of which we applied the lattice structure to improve the wavelet transform shortcomings. In order to enhance the compression by our algorithm, we have compared the results obtained with those of other methods containing wavelet transforms. For this reason, we evaluated two parameters known for their calculation speed. The first parameter is the PSNR; the second is MSSIM (structural similarity) to measure the quality of compressed image. The results are very satisfactory regarding compression ratio, and the computation time and quality of the compressed image compared to those of traditional methods.