Discrete Wavelets with Applications - Spring 2009

Final Project A:
Implementing Matrix Completion for the Daubechies-4 Filter

Prepare a 20 minute presentation. You will be graded on the mathematical correctness of the presentation,  the quality and completeness of  the notebook you prepare, and the quality of your oral presentation. All group members must participate equally in the presentation.

Problem

1. Use Mathematica to present the solution to Problem 7.19 in the textbook.
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. Would a similar procedure be possible for the Daubechies-6 filter? Can you outline such a procedure? (No coding required for Step 5)