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We propose a novel symmetry-based technique for scalable lossless compression of 3D medical image data. The proposed method employs the 2D integer wavelet transform to decorrelate the data and an intraband prediction method to reduce the energy of the sub-bands by exploiting the anatomical symmetries typically present in structural medical images. A modified version of the embedded block coder with optimized truncation (EBCOT), tailored according to the characteristics of the data, encodes the residual data generated after prediction to provide resolution and quality scalability. Performance evaluations on a wide range of real 3D medical images show an average improvement of 15% in lossless compression ratios when compared to other state-of-the art lossless compression methods that also provide resolution and quality scalability including 3D-JPEG2000, JPEG2000, and H.264/AVC intra-coding.