Reversible 3-D decorrelation of medical images

Two methods, namely, differential pulse code modulation (DPCM) and hierarchical interpolation (HINT), are considered. It is shown that HINT cannot be extended straightforwardly to 3-D images as contrasted with DPCM. A 3-D HINT is therefore proposed which is based on a combination of 2-D and 3-D filters. Both decorrelation methods were applied to three-dimensional computed tomography (CT), magnetic resonance (MR), and single-photon-emission CT (SPECT) images. It was found that a 3-D approach is optimal for some studies, while for other studies 2-D or even 1-D decorrelation performs better. The optimal dimensionality of DPCM is related to the magnitudes of the local correlation coefficients (CCs). However, the nonlocal nature of HINT makes the local correlation coefficients useless as indicators of the dimensionality; a better candidate is the image voxel size. For images with cubic or nearly cubic voxels 3-D HINT is generally optimal. For images in which the slice thickness is large compared to the pixel size a 2-D (intraslice) HINT is best. In general, the increase in efficiency obtained by extending 2-D decorrelation method to 3-D is small.