CHUI, Charles

Department of Mathematics
Hong Kong Baptist University
Kowloon Tong, Hong Kong
Telephone: (852) 3411-5148
Facsimile: (852) 3411-5811
Office: FSC1218, Fong Shu Chuen Building, Ho Sin Hang Campus, HKBU
Academic Qualification: Ph. D. (University of Wisconsin, Madison)
Honorary Doctorate (Technical University of Dortmund, Germany)

Brief Biography

Charles K. Chui, Ph.D. Wisconsin-Madison, is Research Professor of Mathematics in Hong Kong Baptist University, while holding a courtesy appointment as Consulting Professor in the Statistics Department of Stanford University. He is also Curators’ Professor Emeritus of the University of Missouri and Distinguished Professor Emeritus of Texas A&M University, where he had joint appointments in four departments of two colleges, namely: Department of Mathematics and Department of Statistics (of the College of Science) and Department of Electrical Engineering and Department of Computer Science (of College of Engineering).

As a leading expert and authority in two mathematical disciplines: Approximation Theory and Computational Harmonic Analysis, Charles is co-Founder with the late Chinese National Academician, Professor Cheng Mende of Peking University, of the “Journal of Approximation Theory and Applications” (now called “Analysis in Theory and Applications”) and is Founder and co-Editor-in-Chief with two U.S. National Academicians, Professor Ronald Coifman (of Yale University) and Professor David Donoho (of Stanford University) of the journal, “Applied and Computational Harmonic Analysis” (ACHA, the flagship journal of the field). In addition, Charles was (or continues to be) editor of 9 other mathematics journals, and was Editor-in-Chief of 3 book series (published by Academic Press, World Scientific, and Elsevier, respectively). He is currently Founding Editor-in-Chief of two book series, “Advances in Mathematical and Engineering Sciences” and “Mathematics Text Books for Sciences and Engineering”, co-published by Atlantis Press and Springer.

Charles has published 370 research papers and 30 books, including 10 research monographs, among which 5 books have been translated into other languages: Chinese, Japanese, and Russian; and his two single-authored books, "An Introduction to Wavelets" and "Multivariate Splines", were the first books in the fields published in the English language. In addition, he co-authored the popular book, "Kalman Filtering: with Real-Time Applications" with his former student, Chair Professor Guanrong Chen of the City University of Hong Kong. This book, published by Springer, has been updated four times, with the fifth edition published in the Spring of 2017. His current research interest is in the discipline of Computational and Applied Mathematics, with focus on real-world data processing, visualization, and understanding, for such big data areas as: blind source decomposition and feature extractions of time series, medical images, surveillance videos, and high-dimensional complex data on certain unknown manifolds of much lower (manifold) dimensions. Some earlier publications can be accessed from here.

After spending over two decades of dedicated research in Function Theory, Approximation Theory, Harmonic Analysis, and Computational Mathematics, Charles turned his attention to the applications of mathematics, particularly in solving real-world problems, first by working on medical imaging in collaboration with a team of Radiologists and Physicists in MD Anderson Cancer Center (in Houston, Texas), followed by founding his first company in the Silicon Valley in California, based on his expertise in image compression and manipulation. This venture led to the founding of a fabless semiconductor startup on the design and manufacture of silicon chips for set-top boxes and HDTV, where Charles played a leading role in technology innovations, by applying mathematics to industrial applications, with other contributions that include development of two industry standards: JPEG-2000 and MPEG-4, as well as several inventions with 38 U.S. patents, mainly on various methods and systems in the imaging and video areas.

Most recently, Charles has turned his attention back to the application of mathematics to the medical field, but now in the area of tele-health care and non-invasive medicine, with focus on separation and isolation of signal signatures of ECG and EEG measurements for visualization and understanding. From discussions with Endocrine specialists and self-study of pulse diagnosis in traditional Chinese medicine (TCM), he has observed the profound similarities between endocrine signal processing of hormone secretion in western medicine the TCM “Qi” circulation, which is believed to be rooted in the kidneys, nourished by the spleen and stomach, and then spread around the entire body by the “energy” of the lungs. Indeed, the TCM “kidney Yin” and “kidney Yan” involve the regulation of the electrolyte balance of sodium and potassium. This is necessary for the circulation of the bio-electrical energy throughout the entire body, with the kidney Yin involving the secret of glucocorticoid hormone from the adrenal cortex, and the kidney Yang involving both the adrenaline secretions of the adrenal medula and other functions, including: hormone secretion of the pituitary and thyroid glands. Charles intends to pursue his study of this important area of TCM in depth, with the goal of bringing the tremendous knowledge, wisdom, and experience in TCM, particularly in pulse diagnosis, to merge with current endocrinology research, and ultimately contributing to early and non-invasive diagnosis to benefit the tele-health and home care sectors.


Research Areas:

Selected (at most 10) Publications of the last three years:

  1. C. K. Chui, S. B. Lin, and D. X. Zhou. Deep neural networks for rotation-invariance approximation and learning. Analysis and Applications , Vol 17 (2019).
  2. C. K. Chui, S. B. Lin, B. Zhang, and D. X. Zhou, Realization of spatial sparseness by deep ReLU nets with massive data. IEEE transactions on Neural Networks and Learning Systems, (2020), accepted for publication.
  3. C. K. Chui, S. B. Lin, and D. X. Zhou. Deep net tree structure for balance of capacity and approximation ability. Frontiers in Applied Math. Statistics, Open Access Journal (2020).
  4. C.K. Chui and H.N. Mhaskar, A unified method for super-resolution recovery and real exponential-sum separation. Applied and Computational Harmonic Analysis, Vol. 46 (2019), 431 - 451.
  5. C.K. Chui, S.B. Lin, and D.X. Zhou, Construction of neural networks for realization of localized deep learning. Frontiers in Applied Math and Statistics, May 17, 2018. (
  6. C. K. Chui and H. N. Mhaskar, Deep nets for manifold learning. Frontiers in Applied Math and Statistics, May 29, 2018. (
  7. C.K. Chui and H.N. Mhaskar, A Fourier-invariant method for locating point-masses and computing their attributes. Applied and Computational Harmonic Analysis, Vol. 45 (2018), 436 - 452.
  8. C. K. Chui, H. N. Mhaskar, and X. S. Zhuang, Representation of functions on big data associated with directed graphs. Applied and Computational Harmonic Analysis, Vol. 44 (2018), 165 – 188.
  9. C. K. Chui, J. De Villiers, and X. S. Zhuang, Multirate systems with shortest spline-wavelet filters. Applied and Computational Harmonic Analysis, Vol. 41 (2016), 266-296.
  10. C. K. Chui and H. N. Mhaskar, Signal decomposition and analysis via extraction of frequencies. Applied and Computational Harmonic Analysis, Vol. 40 (2016), 97-136.

Some earlier publications can be accessed from here

Links with industry or the professional community:

  1. Editor-in-Chief, Applied and Computational Harmonic Analysis (ACHA), Elsevier.
  2. Field Chief Editor, Frontiers in Applied Mathematics and Statistics (FAMS), an open-access journal published by “www.”.
  3. Chief Editor, Mathematics of Computation and Data Science (a section of FAMS).
  4. Book series Editor-in-Chief, Atlantis Studies in Mathematics for Engineering and Science, Atlantis Press, Paris; co-published with Springer.
  5. Book series Editor-in-Chief, Mathematics Textbooks for Science and Engineering, Atlantis Press, Paris; co-published with Springer.
  6. Editor, Journal of Approximation Theory (JAT), Elsevier.
  7. Associate Editor, International Journal of Wavelets, Multiresolution and Information Processing, World Scientific.
  8. Editor, GEM--International Journal on Geomathematics, Springer.