Discrete Wavelets

Final Projects

Helmut  Knaust - Department of Mathematical Sciences, University of Texas at El Paso, hknaust@utep.edu
11/15/2012

Final Project presentation will be during final exam time on Thursday, December 13, at 19:00-21:45 in Bell 130.

Each student group will  give a 20 minute presentation. All electronic material to be presented has to be turned in by Friday, December 14, at 17:00.

Please form three student groups of three students and two student groups of two students. Final project selection will take place on Tuesday, November 20, during class time.

Project A - FBI fingerprint storage
April, Saul

The FBI uses a fixed wavelet packet and a special quantization algorithm to compress fingerprint images for storage.

A description of the algorithm can be found in Ruch & Van Fleet's book.

I will provide the group with a sample fingerprint image. A copy of the book is available for your perusal.

Project B - Smoke Detection
Daniel, Heidi

The paper "CONTOUR BASED SMOKE DETECTION IN VIDEO USING WAVELETS", by B. Ugur Toreyin , Yigithan Dedeoglu and A. Enis Cetin discusses various techniques  - some of them using wavelets - to detect smoke in videos. Some sample videos are available at  http://signal.ee.bilkent.edu.tr/VisiFire/Demo/SampleClips.html. You  will need some software such as VirtualDub to extract the image frames from a video.

Project C - Lossless JPEG2000 with Lifting
Andrew, Jeremy R., Marisol

There is a lossless version of the JPEG2000 algorithm designed for archiving. 

1. Implement  the grayscale algorithm as described in our textbook, pp. 472-479.
2. Implement the color algorithm using Reversible Component Transformation (RCT) - a description can be found in a student paper.

Project D - JPEG Algorithm
Jorge, Otoniel

Explain and implement the JPEG algorithm for grayscale images (see Section 12.1 in the textbook). Research whether there other normalization matrices - what is the rationale for the choice of the coefficients?

Project E - Cascade Algorithm

The Cascade Algorithm can be used to construct approximations to the scaling and wavelet functions using the coefficients of the discrete wavelet algorithm, see Ruch & van Fleet's book. (A copy of the book is available for your perusal.)

Implement the Cascade Algorithm for the Haar, D6 and D12 scaling functions and wavelet functions.

Project F - Fusing grayscale and color images
Austin, Jeremy S.

In remote sensing, the transmission channel can be very "narrow". To conserve bandwidth, the sender may transmit a detailed grayscale image and a small color image of the same scene. It is then up to the sender to fuse the image to obtain a detailed color image. One such fusing procedure is described in Shutao Li, James T. Kwok, Yaonan Wang: Using the discrete wavelet frame transform to merge Landsat TM and SPOT panchromatic images.

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Project G - Matrix Completion
Juana, Thomas

1. Explain the procedure outlined in Problem 7.19 in the textbook, then use Mathematica to present the solution.
2. Write commands similar to “D4” (see DW.m) for the Matrix Completion of the Daubechies-4 Filter developed in Problem 7.19.
3. Check that the matrix generated by your commands in Step 2 is orthogonal.
4. Take a grayscale picture of your choice, apply your transform once to the image, and check on artifacts at the edges of the blur portion of the transformed image. 
5. Can you implement a similar procedure for the D6 filter? The instructions in D6c may be helpful.