Dynamic contrast-enhanced MRI (DCE-MRI) is an imaging protocol where MRI scans are acquired repetitively throughout the injection of a contrast agent. The analysis of dynamic scans is widely used for the detection and quantification of blood brain barrier (BBB) permeability. Extraction of the pharmacokinetic (PK) parameters from the DCE-MRI washout curves allows quantitative assessment of the BBB functionality. Nevertheless, curve fitting required for the analysis of DCEMRI data is error-prone as the dynamic scans are subject to non-white, spatially-dependent and anisotropic noise that does not fit standard noise models. The two existing approaches i.e. curve smoothing and image denoising can either produce smooth curves but cannot guaranty fidelity to the PK model or cannot accommodate the high variability in noise statistics in time and space. We present a novel framework based on Deep Neural Networks (DNNs) to address the DCE-MRI de-noising challenges. The key idea is based on an ensembling of expert DNNs, where each is trained for different noise characteristics and curve prototypes to solve an inverse problem on a specific subset of the input space. The most likely reconstruction is then chosen using a classifier DNN. As ground-truth (clean) signals for training are not available, a model for generating realistic training sets with complex nonlinear dynamics is presented. The proposed approach has been applied to DCE-MRI scans of stroke and brain tumor patients and is shown to favorably compare to state-of-the-art denoising methods, without degrading the contrast of the original images.