ATD: Algorithm, Analysis, and Prediction for Nonlinear and Non-Stationary Signals via Data-Driven Iterative Filtering Methods

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Have you ever wondered how to separate two conversations recorded at the same time in one room or how to identify irregular patterns in a electrocardiogram reading? In signal processing, those tasks are called de-mixing, which is very challenging, especially when the signals are mixed in a time-varying manner (non-stationary), or when they are not simply added together (nonlinear). The standard methods, such as the algorithms based on classical Fourier analysis or wavelets, can work effectively for linear and stationary signals, but are not as satisfactory for nonlinear or non-stationary signals. Developing algorithms that can handle such signals becomes a timely task that inspires a wave of research in recent years. A new method, named adaptive local iterative filtering (ALIF) is proposed in this project. ALIF can decompose a non-stationary and nonlinear signal into finitely many components, each of which is called an intrinsic mode function (IMF) that reflects the local property at a certain frequency. ALIF is a nonlinear process that can be adaptive according to the input signals, and can separate different local features (frequencies) automatically. ALIF will also be used together with a machine learning method called factorization machine (FM) to develop a novel signal prediction strategy. It is expected that the ALIF and its prediction algorithms can be used in various applications such as chemical and biological threat detections, ionospheric radio power scintillation in geophysics, data classification and prediction in social media, and financial data analysis.Nonlinear and non-stationary signals are ubiquitous in real world applications, and they often cannot be handled effectively by the standard algorithms based on Fourier/wavelet transforms, due to the non-linearity and/or their time-varying nature. To capture features, especially the hidden ones, in these signals, it is necessary for the analysis methods to be local, adaptive and stable. The focus of this project has two parts: 1) designing data adaptive algorithms that involve techniques such as iterative filtering for the time frequency analysis; and 2) developing prediction strategies using adaptive iterative filtering techniques in conjunction with the neural networks on nonlinear and non-stationary signals. In the first part, an adaptive local iterative filtering (ALIF) is designed to decompose nonlinear and non-stationary signals, without knowing its instantaneous frequency information in advance. Accompanied with ALIF is a new way, based on dynamical system concepts, to calculate the instantaneous frequencies for decomposed signals. The second part of the project is on a feature prediction strategy, using ALIF together with the factorization machine from neural networks, to learn and predict useful features from noisy signals. In both parts, the mathematical properties, such as convergence and stability of the proposed algorithms, are at the center of studies along with various applications including chemical and biological threat detection, ionospheric radio power scintillation in geophysics, and financial data analysis. The research topic contains a wide range of problems that can be used as projects suitable for undergraduate and graduate education, and postdoctoral scholar training.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.