Using the Haar-Fisz wavelet transform to uncover regions of constant light intensity in Saturn's rings
Saturn's ring system is actually comprised of a multitude of separate rings, yet each of these rings has areas with more or less constant structural properties which are hard to uncover by observation alone. By measuring stellar occultations, data is collected in the form of Poisson counts (of over 6 million observations) which need to be denoised in order to find these areas with constant properties. At present, these areas are found by visual inspection or examining moving averages, which is hard to do when the amount of data is huge. It is also impossible to do this using the changepoint analysis-based method by Scargle (1998, 2005). For the purpose of finding areas of constant Poisson intensity, a state-of-the-art Haar-Fisz algorithm for Poisson intensity estimation is employed. This algorithm is based on wavelet-like transformation of the original data and subsequent denoising, a methodology originally developed by Nason and Fryzlewicz (2005). We apply the HaarFisz transform to the original data, which normalizes the noise level, then apply the Haar wavelet transform and threshold wavelet coefficients. Finally, we apply the inverse Haar-Fisz transform to recover the Poisson intensity function. We implement the algorithm using R programming language. The program was first tested using synthetic data and then applied to original Saturn ring observations, resulting in a quick, easy method to resolve data into discrete blocks with equal mean average intensities.
This item is only available in print in the UCF Libraries. If this is your thesis or dissertation, you can help us make it available online for use by researchers around the world by downloading and filling out the Internet Distribution Consent Agreement. You may also contact the project coordinator Kerri Bottorff for more information.
Bachelor of Science (B.S.)
College of Sciences
Dissertations, Academic -- Sciences;Sciences -- Dissertations, Academic
Length of Campus-only Access
Honors in the Major Thesis
Paulson, Courtney L., "Using the Haar-Fisz wavelet transform to uncover regions of constant light intensity in Saturn's rings" (2010). HIM 1990-2015. 946.