Wavelet Based Methods in Image Processing
S. Allen Broughton
RoseHulman Institute of Technology
Winter Quarter 1998
RHIT Applied Mathematics Seminar
Abstract
It is obvious to all that image (and signal) processing has become an exceedingly
important and hot topic that cuts across many areas: engineering, physical
science, computer science and of course mathematics. Less obvious, but
becoming increasingly well known, is that signal and image processing are
getting great improvements in performance by using wavelet based methods.
In an effort to achieve better understand the wavelet
based methods and image processing itself, I will give a series of talks
that introduce wavelet based image processing methods in the context of
traditional image processing. The plan is to have about four talks that
roughly cover the following:

Introduction to image processing and image processing problems:
restoration, compression and denoising

Filtering and Fourier methods

Localization, wavelet and windowed transforms

Filter bank implementation of wavelet based methods
The talks will, of course, have an underlying mathematical theme, but I
intend to use lots of examples and computer illustrations that Ed Doering
and I have developed in our joint course last fall. The talks should be
accessible to all faculty and most interested undergraduates.
Lecture 1: Introduction to Image Processing
Power
Point Presentation in pdf format
MATLAB Scripts  Image processing toolbox used
Restoration script ansmid3.m
Edge detection script edgedet.m
Blurring 8bit color vs monochrome eightbit.m
Other required scripts showgimg.m,
spcnvmat.m,
Lecture 2: Filtering and Convolution
Power Point Presentation in pdf
format
MAPLE Scripts
Filtering demonstration filter1d.mws
MATLAB Scripts
Uniform motion blur blur.m,
ansmid3.m,
Edge detection edgedet.m,
Lecture 2.a Fourier Transform
Power Point Presentation in pdf
format
MAPLE Scripts
Discrete Model Wave forms waveform.mws,
MATLAB Scripts
1D Fourier transforms dft1demo1.m,dft1demo2.m
2D Fourier transforms dft2demo1.m,dft2demo2.m,dft2demo3.m
Restoration script ansmid3.m
Lecture 3: Localization, wavelets and windowed Fourier transforms
Power Point Presentation in pdf
format
MAPLE Scripts
continuous windowed Fourier transform wft.mws
continuous wavelet transform cwt.mws
MATLAB Scripts
localization problems localdemo.m
Audio spectrogram auspec.m
Lecture 4: Filter banks and wavelets
Now cahpter 7 of this book Discrete Fourier Analysis and Wavelets Applications to Signal and Image Processing
MATLAB Scripts
high pass and low pass decomposition
RoseHulman
Mathematics Department
Contact me at brought@rosehulman.edu
This page last updated on 14 Jun 10.