# Wavelet Based Methods in Image Processing

S. Allen Broughton
Rose-Hulman 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:

1.  Introduction to image processing and image processing  problems: restoration, compression and denoising
2. Filtering and Fourier methods
3. Localization, wavelet and windowed transforms
4. 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 8-bit 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

• Rose-Hulman Mathematics Department

Contact me at brought@rose-hulman.edu