Theoretical Limits of Component Identification in a Separable Nonlinear Least Squares Problem

• Activity Number: 232
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Ross Hilton*+ and Nicoleta Serban
• Companies: Georgia Institute of Technology and Georgia Institute of Technology
• Keywords: component identification ; feature detection ; Mexican Hat wavelet basis ; separable nonlinear least squares problem ; wavelet analysis

Abstract

We provide theoretical insights into component identification in a separable nonlinear least squares problem in which the model is a linear combination of nonlinear functions (called components in this paper). Within this research, we assume that the number of components is unknown. While the vast majority of research for this model focuses on its estimation, the objective of this paper is to understand the limits of component discovery under the assumed model. Particularly, we focus on two aspects. One is sensitivity analysis referring to the ability of separating regression components from noise. The second is resolution analysis referring to the ability of de-mixing components that have similar location parameters. To address these two aspects we use a wavelet transformation that allows to zoom in at different levels of details in the observed data. In deriving the theoretical limits using wavelet analysis, we draw inspiration from many research sources on feature detection including image processing, discrete and continuous wavelet theory for both sharp and smooth signal features.