We introduce a new algorithm for the reconstruction of functional brain activations from near-infrared spectroscopic imaging (NIRSI) data. While NIRSI offers remarkable biochemical specificity, the attainable spatial resolution with this technique is rather limited, mainly due to the highly scattering nature of brain tissue and the low number of measurement channels. Our approach exploits the support-limited (spatially concentrated) nature of the activations to make the reconstruction problem well-posed. The new algorithm considers both the support and the function values of the activations as unknowns and estimates them from the data. The support of the activations is represented using a level-set scheme. We use a two-step alternating iterative scheme to solve for the activations. Since our approach uses the inherent nature of functional activations to make the problem well-posed, it provides reconstructions with better spatial resolution, fewer artifacts, and is more robust to noise than existing techniques. Numerical simulations and experimental data indicate a significant improvement in the quality (resolution and robustness to noise) over standard techniques such as truncated conjugate gradients (TCG) and simultaneous iterative reconstruction technique (SIRT) algorithms. Furthermore, results on experimental data obtained from simultaneous functional magnetic resonance imaging (fMRI) and optical measurements show much closer agreement of the optical reconstruction using the new approach with fMRI images than TCG and SIRT.