Medical imaging technology and applications are continuously evolving, dealing with images of increasing spatial and temporal resolutions, which enable more accurate processing, feature analysis and medical diagnosis. However, the increase in resolution also requires a growing amount of data to be stored, processed and exchanged or transmitted through networks. Despite the high coding efficiency achieved by the most recent image and video coding standards in lossy compression, they are not well suited for quality-critical medical image compression where either near-lossless or lossless coding is required. In this paper we propose a method to improve lossless coding of volumetric medical images, such as Magnetic Resonance and Computed Tomography, and medical sequences such as X-ray Angiography images, using the latest standard High Efficiency Video Encoder (HEVC). New pixel-wise prediction techniques are proposed to extend the current HEVC lossless tools, based on Least-Squares Prediction (LSP). Experimental results show a bitrate reduction of over 44%, when compared to DICOM recommended encoders, and 13.8% when compared to standard lossless HEVC, for 8 bpp volumetric images, and over 8% and 4.6%, respectively, for volumetric images using more than 8 bpp.