Time-frequency analysis in deep learning framework: theory, computation and applications

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Abnormal brain activities or structural vibrations that have a sudden onset and occur at a distinct frequency range, may provide early warnings of abnormal conditions or structural failure. Time-frequency analysis (TFA) is comprised of various mathematical transforms that describe how frequency content evolves with time. Local features are often first extracted from the time-frequency representation of time-varying signals and then feed to the machine learning algorithms for classification and pattern recognition. Thus, integrating TFA into a realtime monitoring and diagnosis system, we can make early detection to prevent expensive and fatal damages. Despite of its usefulness, two main issues severely impede the effectiveness of the TFA based monitoring and diagnoses. First, the computational effort of TFA is often substantial. This is particularly problematic for processing ultra large data set and/or realtime data. Second, many standard TFA techniques use a fixed set of bases/frames to decompose a signal. In practice, many of important applications will generate highly random and timevarying signals. Using the same set of bases/frames to analyze the entire signal may not be effective. In recent years, with the easy access to powerful computing resources, better performance can be obtained using deep learning neural networks in image recognition, manufacturing], disease diagnosis, and speech processing. The main advantages of deep learning network is that it does not require expert knowledge but often produces higher accuracy than the classic methods. But mathematical understanding of deep learning networks is still not yet clear. The main objective of this research program is to theoretically investigate the time-frequency analysis in the deep learning framework and explore whether such a combination can overcome the limitations of existing classic time-frequency analysis. We aim to answer the following questions: 1) Does the deep learning framework of a time-frequency analysis alter the original signal? 2) Can it help to determine an optimal time-frequency representation of a signal dynamically? 3) If so, what are the essential mathematical properties of dynamic timefrequency analysis using deep learning architecture 4) Can we implement fast algorithms to compute such a representation? This research proposal is interdisciplinary and practical. It integrates mathematics, deep learning, computing, and application development. The trainees in the program will work closely with scientists in data science, health care and industries and make significant original contributions relevant to important real world problems. The success of this program will advance time-frequency analysis field, create sophisticated  time-frequency analysis tailored for specific types of signals and lead to the R&D development of computer-assisted monitoring and detection software for various applications.