Non-local spatial regularization of MRI T2 relaxation images for myelin water quantification

Myelin is an essential component of nerve fibers and monitoring its health is important for studying diseases that attack myelin, such as multiple sclerosis (MS). The amount of water trapped within myelin, which is a surrogate for myelin content and integrity, can be measured in vivo using MRI relaxation techniques that acquire a series of images at multiple echo times to produce a T2 decay curve at each voxel. These curves are then analyzed, most commonly using non-negative least squares (NNLS) fitting, to produce T2 distributions from which water measurements are made. NNLS is unstable with respect to the noise and variations found in typical T2 relaxation images, making some form of regularization inevitable. The current methods of NNLS regularization for measuring myelin water have two key limitations: 1) they use strictly local neighborhood information to regularize each voxel, which limits their effectiveness for very noisy images, and 2) the neighbors of each voxel contribute to its regularization equally, which can over-smooth fine details. To overcome these limitations, we propose a new regularization algorithm in which local and non-local information is gathered and used adaptively for each voxel. Our results demonstrate that the proposed method provides more globally consistent myelin water measurements yet preserves fine structures. Our experiment with real patient data also shows that the algorithm improves the ability to distinguish two sample groups, one of MS patients and the other of healthy subjects.