Consider an experimental design of a neuroimaging study, where we need to obtain p measurements for each participant in a setting where p‘ (< p) are cheaper and easier to acquire while the remaining (p – p‘) are expensive. For example, the p‘ measurements may include demographics, cognitive scores or routinely offered imaging scans while the (p – p‘) measurements may correspond to more expensive types of brain image scans with a higher participant burden. In this scenario, it seems reasonable to seek an “adaptive” design for data acquisition so as to minimize the cost of the study without compromising statistical power. We show how this problem can be solved via harmonic analysis of a band-limited graph whose vertices correspond to participants and our goal is to fully recover a multi-variate signal on the nodes, given the full set of cheaper features and a partial set of more expensive measurements. This is accomplished using an adaptive query strategy derived from probing the properties of the graph in the frequency space. To demonstrate the benefits that this framework can provide, we present experimental evaluations on two independent neuroimaging studies and show that our proposed method can reliably recover the true signal with only partial observations directly yielding substantial financial savings.