The Pseudo Projection Operator: Applications of Deep Learning to Projection Based Filtering in Non-Trivial Frequency Regimes

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 MultiModal 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.

[1]  Hubert Cecotti,et al.  Convolutional Neural Network with embedded Fourier Transform for EEG classification , 2008, 2008 19th International Conference on Pattern Recognition.

[2]  Adam Arkin,et al.  On the deduction of chemical reaction pathways from measurements of time series of concentrations. , 2001, Chaos.

[3]  Zhenshan Bing,et al.  Spiking Neural Network for Fourier Transform and Object Detection for Automotive Radar , 2021, Frontiers in Neurorobotics.

[4]  Gaël Varoquaux,et al.  Scikit-learn: Machine Learning in Python , 2011, J. Mach. Learn. Res..

[5]  Randy C. Paffenroth,et al.  Deep Learning with Domain Randomization for Optimal Filtering , 2019, 2019 18th IEEE International Conference On Machine Learning And Applications (ICMLA).

[6]  April S. Brown,et al.  Using neural networks to construct models of the molecular beam epitaxy process , 2000 .

[7]  Kamyar Azizzadenesheli,et al.  Fourier Neural Operator for Parametric Partial Differential Equations , 2021, ICLR.

[8]  Luiz Paulo Lopes Fávero,et al.  Estimation , 2019, Data Science for Business and Decision Making.

[9]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[10]  David S. Wishart,et al.  Bioinformatics Applications Note Systems Biology Metatt: a Web-based Metabolomics Tool for Analyzing Time-series and Two-factor Datasets , 2022 .

[11]  Jeremy Kepner,et al.  Interactive Supercomputing on 40,000 Cores for Machine Learning and Data Analysis , 2018, 2018 IEEE High Performance extreme Computing Conference (HPEC).

[12]  Guigang Zhang,et al.  Deep Learning , 2016, Int. J. Semantic Comput..

[13]  Maneuvering Target Tracking using the Autoencoder-Interacting Multiple Model Filter , 2020, 2020 54th Asilomar Conference on Signals, Systems, and Computers.

[14]  Randy C. Paffenroth,et al.  The Autoencoder-Kalman Filter: Theory and Practice , 2019, 2019 53rd Asilomar Conference on Signals, Systems, and Computers.

[15]  M. Powell,et al.  Approximation theory and methods , 1984 .

[16]  Vivek K Goyal,et al.  Foundations of Signal Processing , 2014 .

[17]  R. A. Silverman,et al.  Special functions and their applications , 1966 .

[18]  Gaurav Sharma,et al.  Creating a Multitrack Classical Music Performance Dataset for Multimodal Music Analysis: Challenges, Insights, and Applications , 2016, IEEE Transactions on Multimedia.

[19]  R. Kennedy,et al.  Hilbert Space Methods in Signal Processing , 2013 .

[20]  T. Soong,et al.  Mathematics of Kalman-Bucy filtering , 1985 .

[21]  Gilbert Helmberg,et al.  Introduction to Spectral Theory in Hilbert Space , 1970 .