Learning Asymmetric and Local Features in Multi-Dimensional Data through Wavelets with Recursive Partitioning
This work addresses the challenge of efficiently processing large-scale images with local details, which is critical for biomedical and natural image applications, though it appears incremental as it builds on existing wavelet methods.
The authors tackled the problem of learning asymmetric and local features in multi-dimensional data like images by developing a probabilistic model-based framework that adapts discrete wavelet transforms through Bayesian hierarchical modeling, achieving linear computational scalability in sample size. They demonstrated its performance in image reconstruction tasks, comparing favorably to state-of-the-art methods on datasets including ImageNet and retinal optical coherence tomography.
Effective learning of asymmetric and local features in images and other data observed on multi-dimensional grids is a challenging objective critical for a wide range of image processing applications involving biomedical and natural images. It requires methods that are sensitive to local details while fast enough to handle massive numbers of images of ever increasing sizes. We introduce a probabilistic model-based framework that achieves these objectives by incorporating adaptivity into discrete wavelet transforms (DWT) through Bayesian hierarchical modeling, thereby allowing wavelet bases to adapt to the geometric structure of the data while maintaining the high computational scalability of wavelet methods---linear in the sample size (e.g., the resolution of an image). We derive a recursive representation of the Bayesian posterior model which leads to an exact message passing algorithm to complete learning and inference. While our framework is applicable to a range of problems including multi-dimensional signal processing, compression, and structural learning, we illustrate its work and evaluate its performance in the context of image reconstruction using real images from the ImageNet database, two widely used benchmark datasets, and a dataset from retinal optical coherence tomography and compare its performance to state-of-the-art methods based on basis transforms and deep learning.