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29 April 2005 Partial volume correction using reverse diffusion
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Many medical images suffer from the partial volume effect where a boundary between two structures of interest falls in the middle of a voxel giving a signal value that is a mixture of the two. We propose a method to restore the ideal boundary by splitting a voxel into sub-voxels and reapportioning the signal into the sub-voxels. We designed this method to correct MRI 2D slice images where partial volume can be a considerable limitation. Each voxel is divided into four (or more) sub-voxels by nearest neighbor interpolation. The gray level of each sub-voxel is considered as “materials” able to move between sub-voxels but not between voxels. A partial differential equation is written to allow the material to flow towards the highest gradient direction, creating a “reverse” diffusion process. Flow is subject to constraints that tend to create step edges. Material is conserved in the process thereby conserving MR signal. The method proceeds until the flow decreases to a low value. To test the method, synthetic images were down-sampled to simulate the partial volume artifact and restored. Corrected images were remarkably closer both visually and quantitatively to the original images than those obtained from common interpolation methods: on simulated data mean square errors were 0.35, 1.09, and 1.24 for the proposed method, bicubic, and bilinear interpolation respectively. The method was relatively insensitive to noise. On MRI physical phantom and brain images, restored images processed with the new method were visually much closer to high-resolution counter-parts than those obtained with common interpolation methods.
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Olivier Salvado, Claudia Hillenbrand, and David L. Wilson "Partial volume correction using reverse diffusion", Proc. SPIE 5747, Medical Imaging 2005: Image Processing, (29 April 2005);

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