Maximum Likelihood Wavelet Density Estimation With Applications to Image and Shape Matching

Density estimation for observational data plays an integral role in a broad spectrum of applications, e.g. statistical data analysis and information-theoretic image registration. Of late, wavelet based density estimators have gained in popularity due to their ability to approximate a large class of functions; adapting well to difficult situations such as when densities exhibit abrupt changes. The decision to work with wavelet density estimators (WDE) brings along with it theoretical considerations (e.g. non-negativity, integrability) and empirical issues (e.g. computation of basis coefficients) that must be addressed in order to obtain a bona fide density. In this paper, we present a new method to accurately estimate a non-negative density which directly addresses many of the problems in practical wavelet density estimation. We cast the estimation procedure in a maximum likelihood framework which estimates the square root of the density p ; allowing us to obtain the natural non-negat...

• Type: Journal
• Year: 2008
• Where: TIP
• Authors: Adrian M. Peter, Anand Rangarajan
• Keywords: Density Estimation, Density Estimators, TIP 2008, Wavelet Density