Wavelet is a novel scientific thought and method that was created in the 1980s and has been rapidly developed and improved. It is a scientific symphony chapter in which many scientists and engineers in the mainstream scientific research field of the contemporary world have contributed their outstanding wisdom to the treasure house of human thought and cognitive methods. The wavelet method has localization capabilities in both the observation domain and the transformation domain. Its wide application has promoted the scientific concepts and ideas, epistemology and computational methods in the main frontier fields of contemporary science and technology, including mathematics, physics, computer science, optics, acoustics, biology and medicine, information science, control science, visual science, quantum theory, astrophysics, management, precision mechanics and aerospace science, into a new era, and has achieved fruitful results and large-scale innovation. Therefore, wavelet theory has enjoyed the reputation of "mathematical microscope".
The course "Wavelets and Science" is aimed at college students, graduate students and scientific researchers in the second year and above in various disciplines such as science, engineering, management, and medicine who have experience in linear algebra and calculus. It plans to introduce typical successful cases of wavelet methods in solving research problems in the mainstream frontier fields of contemporary science and technology through 24 hours of study, to help learners understand and master the scientific ideas and research methods of wavelet core theory, such as wavelets, wavelet multi-resolution analysis, wavelet packets, wavelets and wavelet packet decomposition/synthesis algorithms, etc., to establish new thinking to understand typical frontier problems in contemporary science based on wavelet ideas, and to cultivate and improve learners' innovative research capabilities to use wavelet methods and theories to solve scientific and technological problems.
The main contents of the course "Wavelets and Science" include a brief history of wavelets, basic properties of wavelets and wavelet transforms, wavelet multi-resolution analysis methods, wavelet construction and examples, wavelet packet theory, time-frequency localization of wavelets and wavelet packets, decomposition/synthesis algorithms of wavelets and wavelet packets, wavelet transform and wavelet packet transform of images, wavelet and wavelet packet pyramid algorithms for images, wavelet application topics: wavelet packets and uncertainty principle, wavelets and signal filtering and image filtering, wavelet application topics: wavelets and image compression, etc.