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Wednesday, November 21, 2012

Small-sample brain mapping: sparse recovery on spatially correlated designs with randomization and clustering



Functional neuroimaging can measure the brain’s response to an external stimulus. It is used to perform brain mapping: identifying from these observations the brain regions involved. This problem can be cast into a linear supervised learning task where the neuroimaging data are used as predictors for the stimulus. Brain mapping is then seen as a support recovery problem. On functional MRI (fMRI) data, this problem is particularly challenging as i) the number of samples is small due to limited acquisition time and ii) the variables are strongly correlated. We propose to overcome these difficulties using sparse regression models over new variables obtained by clustering of the original variables. The use of randomization techniques, e.g. bootstrap samples, and hierarchical clustering of the variables improves the recovery properties of sparse methods. We demonstrate the benefit of our approach on an extensive simulation study as well as two publicly available fMRI datasets.
The video presentation is here

GaelAlexandre and I had a small discussion on this issue of RIP being a good condition against which to test any design matrix for sparse recovery (in their case, their measurement matrix is really the fMRI images put in columns)  but what came out of this interesting discussion was the following paper for which I have only an abstract (see below). In it, they tried to make a connection between the scattering transform and fMRI activity, may be some work ought to be undertaken with SIFT or FREAK as a way to find out which one of those models connects better to actual brain activity. And looking at the latest capabilities, then maybe we could go into the dream reconstruction business....wow, just wow....


The scattering transform is a hierarchical signal transformation that has been designed to be robust to signal deformations. It can be used to compute representations with invariance or tolerance to any transformation group, such as translations, rotations or scaling. In image analysis, going beyond edge detection, its second layer captures higher order features, providing a fine-grain dissection of the signal. Here we use the output coefficients to fit blood oxygen level dependent (BOLD) signal in visual areas using functional magnetic resonance imag- ing. Significant improvement in the prediction accuracy is shown when using the second layer in addition to the first, suggesting biological relevance of the features extracted in layer two or linear combinations thereof.




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