REVERSIBLE 3-D DECORRELATION OF MEDICAL IMAGES

The subject of this paper is decorrelation methods for reversible comp ression of three-dimensional medical images. In accordance with the re sults obtained in reversibly decorrelating 2-D images [1], two methods are considered, viz. differential pulse code modulation (DPCM) and hi erarchical interpolation (HINT). It is shown that HINT cannot be exten ded straightforwardly to 3-D images as contrasted with DPCM; a 3-D HIN T is therefore proposed which is based on a combination of 2-D and 3-D filters. Both decorrelation methods have been applied to three-dimens ional CT, MR, and SPECT images. We found that a 3-D approach is optima l for some studies, while for other studies 2-D or even 1-D decorrelat ion performs better. The optimal dimensionality of DPCM is related to the magnitudes of the local correlation coefficients (CC's). When one CC outweights the others clearly, 1-D DPCM in that direction is favora ble. When two CC's outweigh the third, a 2-D approach should be pursue d. We have not derived a rule of thumb, because DPCM decorrelation was inferior to HINT decorrelation for all images considered. The nonloca l nature of HINT makes the local correlation coefficients useless as i ndicators of the dimensionality. A better candidate to suggest a choic e of dimensionality 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 (intras lice) HINT is best. The overall conclusion reads that the increase in efficiency obtained by extending the 2-D decorrelation methods to 3-D is generally small. This conclusion is supported by a variance analysi s of first order DPCM/HINT-like estimators for the class of images wit h an isotropic exponentially decaying autocorrelation function.