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Wavelet
via Matrices and its Applications
in signals and image processing
November 16-21, 2020
On the boundary between mathematics and engineering, wavelet theory shows students and
faculty that mathematics research is still thriving, with essential applications in areas such
as signal processing, image compression, and the numerical solution of differential equations.
The programme will focus on theory and applications of wavelets through matrices and its applications
in signals and image processing, etc. Current research topics like Shearlet, curvelet will also be addressed.
Topics will include, but are not limited to, characterization of wavelets through
a linear transformation, mathematical theory and applications of Haar wavelet & Daubechies
wavelet through FFT and application of low pass filter, high pass filter, p-stage-decomposition, etc.
in signal, image processing and numerical solution of ODE/PDE through MATLAB.
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It is necessary to bring different topics from the undergraduate curriculum and introduce students and faculty
to a developing area in mathematics. Basic wavelet theory is a natural topic of this course. The great success of
wavelets and shearlet mostly lies in their many desired properties such as multiscale structure, sparse representation,
efficient approximation schemes, good time-frequency localization,
and fast computational algorithms. In comparison to traditional wavelets,
shearlet have the desired properties of redundancy for robustness and flexibility for an adaptive custom design.
This allows the Teachers to become aware what are the current frontiers of wavelet
theory and what are the possible further developments and applications of wavelets and framelets.
The participants' knowledge about the course content will be raised to the level such that they will
be able to use wavelets and shearlets for their own applications and research.
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