Voxel data

A benefit to simplifying simulations is that it becomes easier to modify simulation code to investigate pulse sequence parameter ranges or to troubleshoot mismatches with actual data. However, sometimes additional levels of physics or programming complexity are necessary to accurately simulate the MRS data. This is particularly true for high SNR single voxel data and metabolite edited MRS data at higher fields where more spectral detail can be seen. 

In the current implementation, G is computed along with normals from two-level (binary) voxel data of snow. For each surface voxel ... 

We use a method that implements the Unbiased Prediction Risk criterion [13] to provide a data-driven approach for the selection of the regularization parameter. The equality constraints are handled with LQ factorization [14] and an iterative method suggested by Villalobos and Wahba [15] is used to incorporate the inequality constraints [10]. The method is well suited for the relatively large-scale problem associated with analyzing each image voxel as no user intervention is required and all the voxels can be analyzed in parallel. 

Fig. 4.1.3 Intrinsic magnetization determined by the relaxation data corresponding to the selected voxel in the Bentheimer sample.

Fig. 4.1.7 Superficial average velocity data for the flow experiment with the thin Bentheimer sandstone sample. Each arrow represents the direction and relative magnitude of the superficial average velocity at the corresponding voxel. The velocities are measured for 58 x 20 voxels.

Fig. 5.2.3 Identification of rivulets and surface wetting in a packing of 5-mm diameter glass spheres contained within a column of inner diameter 40 mm. The data were acquired in a 3D array with an isotropic voxel resolution of 328 xm x 328 pm x 328 [im. (a) The original image of trickle flow is first binary gated, so that only the liquid distribution within the image is seen (white) gas-filled pixels and pixels containing glass spheres show up as zero intensity (black), (b) The liquid distribu-...

Fig. 15. 2-D slice sections through 3-D MR images of water distribution within an initially water-saturated packing of 500-pin glass spheres. Voxel resolution is 94 pm x 94 pm x 94 pm. Data are shown before drying commenced and at three time intervals during the drying process. Only the water within the inter-particle space of the bead packing was imaged (white pixels). No signal was obtained from the solid and gas phases present.

The Euler number may easily be calculated from the voxel-based data set of a 3D reconstruction. For example, the test object is fragmented into voxels, each of them representing a single solid itself. It is possible to compute the 3D morphological parameters of these solids by taking into account the following basic rule ... 

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