Hybrid compression techniques are used to improve the compression efficiency in case of medical images. In region of interest based hybrid compression, the image is divided into foreground which contains diagnostically important areas such as tumor in case of brain MRI images and the remaining is the background region. The technique performs lossless coding of ROI while the background is heavily compressed. Thus the quality of image is preserved with higher compression. A hybrid compression scheme is presented for the compression of brain MRI images. The ROI part is encoded using arithmetic coding while the background region undergoes lossy SPIHT compression. The hybrid method is evaluated in terms of Peak Signal to Noise Ratio (PSNR), Structural Similarity Index (SSIM) and Virtual Information Fidelity (VIF) for various brain MRI images.