We investigate the feasibility of reconstructing a signal recorded at multiple sensors through dispersive channels, with minimal prior information regarding the signal and the channels. We first demonstrate the efficacy of a parallelizable frequency domain algorithm which exploits the continuity of the channels across frequency, operating over small, overlapped frequency bins. The algorithm employs SVD-based estimates of the signal over each frequency bin (over which the channels are modeled as quadratic), and then stitches these estimates together based on consistency conditions across adjacent bins. While this algorithm gives excellent signal reconstruction over frequency bands that are one order of magnitude larger than the channel “coherence bandwidth,” fundamental limitations arise for larger frequency bands, in that it is possible to construct multiple explanations consistent with the recorded data.