Pattern extraction and synthesis using a hierarchical wavelet-based framework

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 (template learning from atomic representations), a novel template learning algorithm with linear complexity. TEMPLAR employs minimum description length (MDL) 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.