Lossless PDE-based Compression of 3D Medical Images

Abstract

Inpainting with Partial Differential Equations (PDEs) has previously been used as a basis for lossy image compression. For medical images, lossless compression is often considered to be safer, given that even subtle details could be diagnostically relevant. In this work, we introduce a PDE-based codec that achieves competitive compression rates for lossless image compression. It is based on coding the differences between the original image and its PDE-based reconstruction. These differences often have lower entropy than the original image, and can therefore be coded more efficiently. We optimize this idea via an iterative reconstruction scheme, and a separate coding of empty space, which takes up a considerable fraction of the field of view in many 3D medical images. We demonstrate that our PDE-based codec compares favorably to previously established lossless codecs. We also investigate the individual benefit from each ingredient of our codec on multiple examples, explore the effect of using homogeneous, edge enhancing, and fourth-order anisotropic diffusion, and discuss the choice of contrast parameters.