Signal estimation from functional magnetic resonance imaging data (fMRI) is a difficult and challenging task that involves carefully chosen models that can be validated by domain experts. This paper explores constrained tensor decomposition methods for model-free estimation of signals from task fMRI. Using a number of constrained tensor decompositions, the signals are estimated as Rank -1 tensor(s). The mutli-subject fMRI data is stored as a three-way tensor (voxel times time times subject). First, the signal is decomposed using traditional PARAFAC modeling. Second, the spatio-temporal maps in the PARAFAC formulation are constrained to be non-negative. Third, using domain knowledge of brain activation pattern in spatial domain for fMRI and loading of the spatio-temporal maps of each individual the paper proposes an optimization model for solving the signal estimation problem from task fMRI data. Three different optimization techniques are also used for solving the optimization problems. The decomposed signal portion includes the brain spatial activation maps and corresponding time courses for each individual during task. The solutions of the optimization are evaluated based on similarity of the task signal (the ground truth) to time courses of the decomposed signal as well as by inspecting the spatial maps visually.