University of St. Thomas Center for Applied Mathematics
Important Dates
Solving for Daubechies Length 4 Filter
Wednesday, February 6, 2008
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Inner Products and Norms
- You may work with a partner if you wish.
- You may work with a partner if you wish.
- You may work with a partner if you wish.
- Click here for more details.
- Click here for more details.
- Spring Break
- Spring Break
- Spring Break
- Easter Break
- You may work with a partner on this lab if you wish (recommended!).
- Click here for more details.
- You may work with a partner on this lab if you wish.
- You may work with a partner on this lab if you wish.
- Click here for more details.
- 8:00am - 10:00am
- Ronald Coifman suggested to Daubechies that orthogonal filters could be designed so that the Fourier transform H(w) of the filter has vanishing derivatives at w=0. Daubechies worked out a process for constructing these filters and named them Coiflets in honor of Coifman. In this project, you will learn how to derive Coiflets. Section 8.3 will serve as a reference. To test their effectiveness in signal denoising, you will compare Coiflet filters to the D4 and D6 filters used in Lab 9.2.
- One of the most useful applications of wavelets is in the area of signal/image denoising. A method developed by Donoho and Johnstone to perform denoising is called Wavelet Shrinkage. We learned about this method in Lab 9.2. In this project, you will learn about a more sophisticated technique for performing denoising called SUREShrink. Section 9.3 will serve as a reference for you. Some knowledge of statistics is required for this project. You will learn how SUREShrink works and then use it to denoise some test signals and images.