Paper:
Unified representation of tractography and diffusion-weighted MRI data using sparse multidimensional arrays
Recently, linear formulations and convex optimization methods have been proposed to predict diffusion-weighted Magnetic Resonance Imaging (dMRI) data given estimates of brain connections generated using tractography algorithms. The size of the linear models comprising such methods grows with both dMRI data and connectome resolution, and can become very large when applied to modern data. In this paper, we introduce a method to encode dMRI signals and large connectomes, i.e., those that range from hundreds of thousands to millions of fascicles (bundles of neuronal axons), by using a sparse tensor decomposition. We show that this tensor decomposition accurately approximates the Linear Fascicle Evaluation (LiFE) model, one of the recently developed linear models. We provide a theoretical analysis of the accuracy of the sparse decomposed model, LiFE SD , and demonstrate that it can reduce the size of the model significantly. Also, we develop algorithms to implement the optimization solver using the tensor representation in an efficient way. *

Review:
The paper propose an efficient approximation of the "Linear Fascicle Evaluation model" (LiFE), which is used for tractography. The key issue with the LiFE model is that it computationally scales poorly such that it is impractical to analyze MRI data at full resolution. The authors propose a sparse approximation based on a Tucker model (tensor model). The authors prove that the approximation is both good and achieves a high compression; this is further evaluated experimentally. The model appears solid and likewise for the analysis. My key objection to the paper is that the actual evaluation of the model for tractography is treated very superficially (just a couple of lines of text). I understand that within the tight boundaries of a NIPS paper, the authors does not have much space for such an evaluation, so I'm willing to forgive this limitation of the paper.
Other than that, the paper is very well written with intuitive figures guiding the reader along the way. As a non-expert, I found the paper a please to read. I do stress that I'm not an expert in neither tractography or tensor models.
A few minor comments (not important in the rebuttal):
*) In line 36, the authors point out that tractography is poorly understood and that competing methods can give wildly different results. The authors then argue that this motivates convex models. I don't buy this argument -- the reason different models give different results is more likely due to different modeling assumptions, rather than whether a global optimum has been found or not.
*) After the propositions: the authors take the time to explain in plain words the key aspects of their propositions. Most authors neglect this, and I just want to say that such efforts make the paper much easier to read. So: thank you!
*) In line 195, you write: "...dataset Fig. 4.a." There's something wrong with that sentence. Perhaps the figure reference should be in a parenthesis?
*) In line 202: typo: "aproach" --> "approach".
== Post rebuttal ==
I have read the other reviews and the rebuttal, and stand by my evaluation that this paper should be accepted.