  The prediction and selection of lesion features are two important tasks in
voxel-based neuroimage analysis. Existing multivariate learning models take two
tasks equivalently and optimize simultaneously. However, in addition to lesion
features, we observe that there is another type of feature, which is commonly
introduced during the procedure of preprocessing steps, which can improve the
prediction result. We call such a type of feature as procedural bias.
Therefore, in this paper, we propose that the features/voxels in neuroimage
data are consist of three orthogonal parts: lesion features, procedural bias,
and null features. To stably select lesion features and leverage procedural
bias into prediction, we propose an iterative algorithm (termed GSplit LBI) as
a discretization of differential inclusion of inverse scale space, which is the
combination of Variable Splitting scheme and Linearized Bregman Iteration
(LBI). Specifically, with a variable the splitting term, two estimators are
introduced and split apart, i.e. one is for feature selection (the sparse
estimator) and the other is for prediction (the dense estimator). Implemented
with Linearized Bregman Iteration (LBI), the solution path of both estimators
can be returned with different sparsity levels on the sparse estimator for the
selection of lesion features. Besides, the dense the estimator can additionally
leverage procedural bias to further improve prediction results. To test the
efficacy of our method, we conduct experiments on the simulated study and
Alzheimer's Disease Neuroimaging Initiative (ADNI) database. The validity and
the benefit of our model can be shown by the improvement of prediction results
and the interpretability of visualized procedural bias and lesion features.
