We consider the ill-posed inverse problem encountered in perfusion magnetic resonance imaging (MRI) analysis due to the necessity of eliminating, via a deconvolution process, the imprint of the arterial input function on the MR signals. Until recently, this deconvolution process was realized independently voxel by voxel with a sole temporal regularization despite the knowledge that the ischemic lesion in acute stroke can reasonably be considered piecewise continuous. A new promising algorithm incorporating a spatial regularization to avoid spurious spatial artifacts and preserve the shape of the lesion was introduced . So far, the optimization of the spatio-temporal regularization parameters of the deconvolution algorithm was supervised. In this communication, we evaluate the potential of the L-hypersurface method in selecting the spatio-temporal regularization parameters in an unsupervised way and discuss the possibility of automating this method. This is demonstrated quantitatively with an in silico approach using digital phantoms simulated with realistic lesion shapes.