A multivariate sparse deconvolution algorithm for multi echo fMRI

This thesis presents a novel algorithm for the deconvolution of multi echo fMRI data with no prior information on the timings of the neuronal events. Based on previous work on the field, a new signal model is proposed in order to take the processing from a voxelwise analysis to an entire brain one. Different proximal operators have been studied for solving the optimisation problem present in the deconvolution, since it is an ill-posed inverse problem, and a novel method based on the stability selection procedure has been suggested to answer to the choice of the regularization parameter dilemma. The method takes advantage of the area under the curve (AUC) of the stability paths to avoid the selection of a single regularization parameter. An optimal approach for the thresholding of AUC timeseries is studied and different debiasing methods for removing the sparsity in prolonged events are presented. The results demonstrate that the MvMESPFM algorithm provides promising results when estimating neuronal-related events even on noisy data. Subject to being thoroughly tested on experimental data, testing conducted on simulated signals suggests that the tool could eventually be introduced to the processing pipelines of different research lines regarding fMRI data analysis.