A Unified Computational Framework for Deconvolution to Reconstruct Multiple Fibers From Diffusion Weighted MRI

Abstract

Diffusion magnetic resonance imaging (MRI) is a relatively new imaging modality which is capable of measuring the diffusion of water molecules in biological systems noninvasively. The measurements from diffusion MRI provide unique clues for extracting orientation information of brain white matter fibers and can be potentially used to infer the brain connectivity in vivo using tractography techniques. Diffusion tensor imaging (DTI), currently the most widely used technique, fails to extract multiple fiber orientations in regions with complex microstructure. In order to overcome this limitation of DTI, a variety of reconstruction algorithms have been introduced in the recent past. One of the key ingredients in several model-based approaches is deconvolution operation which is presented in a unified deconvolution framework in this paper. Additionally, some important computational issues in solving the deconvolution problem that are not addressed adequately in previous studies are described in detail here. Further, we investigate several deconvolution schemes towards achieving stable, sparse, and accurate solutions. Experimental results on both simulations and real data are presented. The comparisons empirically suggest that nonnegative least squares method is the technique of choice for the multifiber reconstruction problem in the presence of intravoxel orientational heterogeneity.

Estimating Orientation Distribution Functions with Probability Density Constraints and Spatial Regularity

“…Even though CSD reduces the occurrence of negative values, it does not completely eliminate them. A more recent method [14] eliminates the negative values by minimizing a nonnegative least-squares cost function. A third limitation of existing QBI methods is that the ODF at each voxel is estimated independently of the information provided in the spatial neighborhood.…”

Structured sparsity for spatially coherent fibre orientation estimation in diffusion MRI

“…The reader can refer to Jian and Vermuri (2007) for a more detailed overview on SD methods and the formal 75 equations describing the relationship between the FOD and the diffusion signal. We consider a dictionary Φ that spans a set of the Diffusion Basis Functions introduced by Ramirez-Manzanares et al (2007).…”

“…It applies Tikhonov regularisation, introducing a constraint on the 2 norm of the FOD, specially to ensure its positivity. Apart from the aforementioned work, most of the state-of-theart methods to solve SD problems promote sparse regularisation based on 1 minimisation (Jian and Vermuri, 2007;Ramirez-Manzanares et al, 2007;Mani et al, 2014), 40 where the 1 norm is defined, for any real vector, as the sum of the absolute value of its coefficients. Yet, Daducci et al (2014b) acknowledge in recent work that 1 minimisation is formally inconsistent with the fact that the volume fraction sum up to unity, and demonstrate the superiority of 0 -norm minimisation.…”

Estimation of Non-negative ODFs Using the Eigenvalue Distribution of Spherical Functions

“…However, existing ODF estimation methods based on a spherical harmonic (SH) representation of the ODF [1][2][3][4][5][6][7][8][9] do not enforce the non-negativity constraint. As a consequence, due to noise and low order SH representation, the estimated ODFs may contain negative values.…”