The advent of new brain imaging techniques such as resting-state functional MRI (fMRI), has led to the need for new approaches to recover brain functional activations without a prior knowledge on the experimental paradigm, as it was the case for task-fMRI. Conventional methods, i.e. the general linear model, requires the knowledge of the task paradigm to estimate the contribution of each voxel's time course to the given task. To overcome this limitation, approaches to deconvolve the blood-oxygen-leveldependent (BOLD) response and recover the underlying neural activations without necessity of prior information has been proposed. Supposing the brain activates in constant blocks, frst we propose a temporal regularized deconvolution technique which uses an exponential operator, whose shape and performance can be adjusted, into a least absolute shrinkage and selection operator (LASSO) model solved via the Least-Angle Regression (LARS) algorithm. We reduced the number of parameters to be set by the user, when compared with the state of the art. Second, we introduce a paradigm-free regularization algorithm that applies on the 4-D fMRI image, acting simultaneously in the 3-D space and the 1-D time dimensions. The approach is based on the idea that large image variations should be preserved as they occur during an activation, whereas small variations should be smoothed to remove noise. It allows to smooth the whole fMRI image with an anisotropic regularization, thus blindly recovering the location of the brain activations in space and their timing and duration.Both approaches were tested on phantom and real data and were demonstrated to improve the results obtained in the state of the art.