Functional magnetic resonance imaging (fMRI) is a non-invasive tomographic imaging modality that has provided insights into systems-level brain function. New analysis methods are emerging to study the dynamic behavior of brain activity. The innovation-driven co-activation pattern (iCAP) approach is one such approach that relies on the detection of timepoints with significant transient activity to subsequently retrieve spatially and temporally overlapping large-scale brain networks. To recover temporal profiles of the iCAPs for further time-resolved analysis, spatial patterns are fitted back to the activity-inducing signals. In this crucial step, spatial dependencies can hinder the recovery of temporal overlapping activity. To overcome this effect, we propose a novel back-projection method that optimally fits activity-inducing signals given a set of transient timepoints and spatial maps of iCAPs, thus taking into account both spatial and temporal constraints. Validation on simulated data shows that transient-based constraints improve the quality of fitted time courses. Further evaluation on experimental data demonstrates that over- and underfitting are prevented by the use of optimized spatio-temporal constraints. Spatial and temporal properties of resulting iCAPs support that brain activity is characterized by the recurrent co-activation and co-deactivation of spatially overlapping large-scale brain networks. This new approach opens new avenues to explore the brain's dynamic core.