Time-frequency analysis in biomedicine: mathematical, computational, and application aspects

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The rapid development of medical imaging technologies has led to many important applications, including computer-aided disease detection, an important component of clinical routine. Due to the inherent time/space variability of biomedical data, producing high quality information for disease diagnosis presents challenges in terms of data analysis and processing. These challenges in turn require the development of innovative theories and methods for optimal data representation. One key methodology in this area is time-frequency analysis. It provides a data representation that simultaneously reveals time and frequency variations and is excellent for data analysis and feature detection.The ultimate goal of my research program is to further develop time-frequency analysis techniques for biomedical applications. This research proposal is to continue the studies on the Stockwell and Hilbert-Huang transforms. Both transforms has had increasing popularity in signal and image processing community for applications in geophysics, engineering, oceanology, and biomedicine.  However, since both transforms represent recent research that originated from applications, a large number of fundamental questions remain in terms of their mathematical foundations, improvement of numerical computations, development of applications. Therefore, the objectives of this research are threefold: 1) provide a more thorough understanding of mathematical framework of the Stockwell and Hilbert-Huang transforms, 2) develop efficient and robust means to compute the transforms so that they can be more practical, and 3) identify important biomedical applications that can benefit from these advanced techniques and design new algorithms tailored for specific applications. This proposal is novel, multi-components and interdisciplinary, the results of which will uniquely combine the theoretical advancements in mathematics and numerical computation to provide better solutions for a wide range of challenging problems in biomedicine and other fields.