Short term Course on

Wavelet via Matrices and its Applications
in signals and image processing

November 16-21, 2020

Discipline of Mathematics, IIT Indore

Overview of the the proposed event

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.

How will this short-term course going to benefit Teachers?

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.  

    Talk by:

    Dr. Bhupendra Singh, Scientist, CAIR-DRDO, Bangalore

    Prof. Bin Han, University of Alberta, Canada

    Dr. Gajendra Kumar Vishwakarma, IIT Dhanbad

    Prof. Hans Georg Feichtinger, University of Vienna, Austria

    Prof. Ivan Slapnicar, University of Split, Croatia

    Dr. Mani Mehera, IIT Delhi

    Dr. Niraj Kumar Shukla, IIT Indore

    Dr. Rajesh Kumar Pandey, IIT Bhu

    Prof. Ram Bilas Pachori, IIT Indore

    Dr. Sk. Safique Ahmad, IIT Indore


  • Diagonalization of Linear Transformations and Matrices

  • Eigen Value, Eigen Vector and Singular Value Decomposition

  • Matrix representation of Discrete Fourier transform (DFT) and Fast Fourier transform (FFT)

  • Complexity of computing the DFT and FFT

  • Time-Frequency Localized Bases & Discrete Wavelet Transforms & Filter Banks

  • Matrix representation of Haar & Daubechies scaling functions and Wavelets

  • Application of low pass filter, high pass filter, pth-stage-decomposition, etc.

  • Complexity of computing the pth-stage wavelet filter bank

  • Continuous Fourier and Wavelet transform, Multiresolution Analysis

  • Recent development of wavelets & shearlets for detection of singularity

  • Matlab implementation of Pseudo inverse of a matrix, DFT, FFT, Convolution, wavelet, etc.

  • Other special lectures, also.

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