  Traditional frequency based projection filters, or projection operators (PO),
separate signal and noise through a series of transformations which remove
frequencies where noise is present. However, this technique relies on a priori
knowledge of what frequencies contain signal and noise and that these
frequencies do not overlap, which is difficult to achieve in practice. To
address these issues, we introduce a PO-neural network hybrid model, the Pseudo
Projection Operator (PPO), which leverages a neural network to perform
frequency selection. We compare the filtering capabilities of a PPO, PO, and
denoising autoencoder (DAE) on the University of Rochester Multi-Modal Music
Performance Dataset with a variety of added noise types. In the majority of
experiments, the PPO outperforms both the PO and DAE. Based upon these results,
we suggest future application of the PPO to filtering problems in the physical
and biological sciences.
