**
**

**A restriction-spectrum sparse-fascicle model for diffusion MRI**

**
**### Ariel Rokem*, Christian Pötter, Robert F. Dougherty

Center for Cognitive and Neurobiological Imaging, Stanford University

*Now at the University of Washington eScience Institute
**
**## RS-SFM Combines two different ideas:

### Sparse Fascicle Model (Rokem et al., 2015)

** The signal is modeled as a combination of tensor response functions: **

...

The active set of 'fascicles' is selected using non-negative least-squares
regression regularized with Elastic
Net

The direction-independent ("isotropic") signal is modeled separately as a
multi-exponential:
$$f(b) = \beta_1 e^{-bD_1} + \beta_2 e^{-bD_2} + \epsilon$$
**
**### Restriction Spectrum Imaging (White et al. 2013)

Each fascicle is repeated with different combinations of λ1,λ2,3
Accounts for different restriction conditions within each voxel
A multi-exponential decay profile for every fascicle
### Results (low gradient strength):

### But also (high gradient strength):

$$Still, \: overall \: R^2 = 98.8$$
## Reproducible research

"...an article about computational result is advertising, not
scholarship. The actual scholarship is the full software environment, code and
data, that produced the result..." -- Buckheit and Donoho (1995)

All the code used to fit the model is available at