Hierarchical wavelet-based image model for pattern analysis and synthesis

Abstract

Despite their success in other areas of statistical signal processing, current wavelet-based image models are inadequate for modeling patterns in images, due to the presence of unknown transformations inherent in most pattern observations. In this paper we introduce a hierarchical wavelet-based framework for modeling patterns in digital images. This framework takes advantage of the efficient image representations afforded by wavelets, while accounting for unknown pattern transformations. Given a trained model, we can use this framework to synthesize pattern observations. If the model parameters are unknown, we can infer them from labeled training data using TEMPLAR, a novel template learning algorithm with linear complexity. TEMPLAR employs minimum description length complexity regularization to learn a template with a sparse representation in the wavelet domain. We illustrate template learning with examples, and discuss how TEMPLAR applies to pattern classification and denoising from multiple, unaligned observations.