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.

中文翻译：

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通过递归分区的小波学习多维数据中的不对称和局部特征


有效学习图像和多维网格上观察到的其他数据中的不对称和局部特征是一个具有挑战性的目标，对于涉及生物医学和自然图像的广泛图像处理应用至关重要。它需要对局部细节敏感的方法，同时足够快来处理大量尺寸不断增加的图像。我们引入了一种基于概率模型的框架，该框架通过贝叶斯分层建模将适应性纳入离散小波变换（DWT）中，从而允许小波基适应数据的几何结构，同时保持小波方法的高计算可扩展性，从而实现这些目标。与样本大小成线性关系（例如图像的分辨率）。我们推导出贝叶斯后验模型的递归表示，从而产生精确的消息传递算法来完成学习和推理。虽然我们的框架适用于包括多维信号处理、压缩和结构学习在内的一系列问题，但我们使用 ImageNet 数据库（两个广泛使用的基准数据集）中的真实图像来说明其工作并评估其在图像重建背景下的性能，以及来自视网膜光学相干断层扫描的数据集，并将其性能与基于基础变换和深度学习的最先进方法进行比较。