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Math 297: Fall 2004
Introduction to Fourier and wavelet analysis with applications to
image reconstruction. |
Instructor: Doug Hardin
Office: SC 1412 (fourth floor of Math Building)
Phone: 2-6662
Email: doug.hardin@vanderbilt.edu
Office Hours: MWF 2:10--3:00 and others by appointment.
Mathematical Files:
- denoise.nb
contains an introduction to ideal low pass filters, denoising, and the Wiener filter.
- GramSchmidt.nb
contains tools for constructing projections and orthonormal bases.
- CircularConv.nb:
a mathematica notebook defining a function that performs a circular convolution of a (short filter) h with a
(possibly long) sample x. An offset for the filter can also be specified. The syntax
is circonv({h,offset},x).
- Wavelet1D.nb: Some routines (and examples) implementing a 1-d wavelet transform.
- WaveletRoutinesExamples.nb: Final Class
Matlab Files:
Subroutines required for Wavelet Transform m-files:
The first three files contain routines used in the remaining files. The file ``wavefilters.m'' contains some basic wavelet
filters.
- circonv.m:
a matlab function for performing a circular convolution of a (short filter) h with a
(possibly long) sample x. An offset for the filter can also be specified. The syntax
is circonv(h,x,offset). The command works columnwise.
- wavedec.m:
An m-file that contains a matlab function implementing a single level wavelet transform.
- waverec.m:
An m-file that contains a matlab function implementing a single level inverse wavelet transform.
- wavefilters.m:
An m-file containing definitions of some wavelet filters. (Note new definitions will be added to this file.)
Wavelet Transforms
- WT.m:
An m-file that contains a matlab function implementing a multilevel wavelet transform.
- IWT.m:
An m-file that contains a matlab function implementing an inverse multilevel wavelet transform.
The file contains subroutines for down sampling and one level transforms.
- WT2D.m:
A 2D wavelet transform function.
- IWT2D.m:
An m-file that contains a matlab function implementing an inverse multilevel wavelet transform.
The file contains subroutines for down sampling and one level transforms.
- WT3D.m:
A 3D wavelet transform function.
Miscellaneous Wavelet Transform m-files:
- hw4.m:
contains matlab commands for problem 4 of homework 4.
- waveshow.m:
shows a 2-d wavelet transform in 4 separate sub-images.
- hw4.m:
performs the ``cascade'' algorithm for a given wavelet filter.