Multiscale Image Analysis and Maximum Penalized Likelihood Estimators

• Activity Number: 29
• Type: Invited
• Date/Time: Sunday, August 11, 2002 : 4:00 PM to 5:50 PM
• Sponsor: Section on Physical & Engineering Sciences*
• Author(s): Robert Nowak*+
• Affiliation(s): Rice University
• Keywords: wavelets ; multiscale analysis ; penalized likelihood ; minimax bounds ; nonparametric estimation ; image reconstruction

Abstract

Wavelet analysis has led to recent breakthroughs in statistical signal and image processing. Despite the success of wavelets, several key issues are not adequately handled by conventional wavelet-based statistical methods, including non-Gaussian observations, two-dimensional singularities (edges), and ill-posed inverse problems. This talk presents our recent efforts to address these limitations. Multiscale likelihood factorizations and maximum penalized likelihood estimators lead to minimal risk bounds for certain non-Gaussian observation models (including Poisson and multinomial). Multiscale image representations based on a new atomic function called platelets (localized functions at various scales, locations, and orientations) provide fast algorithms for accurately approximating and estimating images consisting of smooth regions separated by smooth boundaries. More general inverse problems, which cannot be dealt with by simple wavelet-based methods, are tackled using the new multiscale estimators in combination with a computationally efficient Expectation-Maximization (EM) algorithm. Biomedical imaging problems demonstrate the application of these methods.