A multiscale framework for blind separation of linearly mixed signals
The Journal of Machine Learning Research
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The intensity value of each voxel in a Brain MR image is considered to be a linear combination of signal intensities emitted from protons in aqueous and lipid environments inside that voxel. A novel model describing the Proton Density (PD) and fraction of protons in aqueous environment (Water Fraction - WF) as independent sources of an MR image is suggested. We consider an input set of registered T1 and T2 weighted images to be the mixtures. The sources are separated from these mixtures by applying a geometrical Blind-Source-Separation technique on Sparse projection of the mixtures. A novel model is proposed to relate between the observed scatter-plot and the actual orientations of the mixing matrix and its estimation. The resulting PD source-image is compared to available PD weighted image of the same patient. WF image is used for anatomic classification of the image into brain tissues - White Matter (WM), Grey Matter (GM), and Cerebrospinal Fluid (CSF).