Functional imaging serves as an important supplement to anatomical imaging modalities such as MR and CT in modern health care. In perfusion CT (CTP), hemodynamic parameters are derived from the tracking of the first-pass of the contrast bolus entering a tissue region of interest. In practice, however, the post-processed parametric maps tend to be noisy, especially in low-dose CTP, in part due to the noisy contrast enhancement profile and oscillatory nature of results generated by current computational methods. In this paper, we propose a sparsity-based perfusion parameter deconvolution approach that consists of a non-linear processing based on sparsity prior in terms of residue function dictionaries. Our simulated results from numerical data and experiments in aneurysmal subarachnoid hemorrhage patients with clinical vasospasm show that the algorithm improves the quality and reduces the noise of the perfusion parametric maps in low-dose CTP, compared to state-of-the-art methods.