Diffuse optical imaging is a non-invasive technique that uses near-infrared light to measure changes in brain activity through an array of sensors placed on the surface of the head. Compared to functional MRI, optical imaging has the advantage of being portable while offering the ability to record functional changes in both oxy- and deoxy-hemoglobin within the brain at a high temporal resolution. However, the reconstruction of accurate spatial images of brain activity from optical measurements represents an ill-posed and underdetermined problem that requires regularization. These reconstructions benefit from incorporating prior information about the underlying spatial structure and function of the brain. In this work, we describe a novel image reconstruction approach which uses surface-based wavelets derived from structural MRI to incorporate high-resolution anatomical and structural prior information about the brain. This surface-based approach is used to approximate brain activation patterns through the reconstruction and presentation of topographical (two-dimensional) maps of brain activation directly onto the folded surface of the cortex. The set of wavelet coefficients is directly estimated by a truncated singular-value decomposition based pseudo-inversion of the wavelet projection of the optical forward model. We use a reconstruction metric based on Shannon entropy which quantifies the sparse loading of the wavelet coefficients and is used to determine the optimal truncation and regularization of this inverse model. In this work, examples of the performance of this model are illustrated for several cases of numerical simulation and experimental data with comparison to functional magnetic resonance imaging.