Bayesian hierarchical dictionary learning
Bayesian hierarchical dictionary learning
复制标题
DOI：
10.1088/1361-6420/acad21
复制
发表时间：
2022-12
期刊：
影响因子：
2.1
通讯作者：
Nathan Waniorek;D. Calvetti;E. Somersalo
中科院分区：
文献类型：
--
作者：
Nathan Waniorek;D. Calvetti;E. Somersalo
字典学习的目的是用字典中的原子来表示一个信号，它已经得到了广泛的应用，包括但不限于图像去噪、人脸识别、遥感、医学成像和特征提取。字典学习可以被视为一种可能的数据驱动替代方案，通过识别具有可能输出的数据来解决逆问题，这些输出要么是使用正演模型生成的数字输出，要么是对照实验的早期观察结果。当已知底层信号可以用给定基中的几个向量表示时，稀疏字典学习特别有趣。在本文中，我们提出使用层次贝叶斯模型进行稀疏字典学习，可以捕获底层信号的特征，例如稀疏表示和非负性。同样的框架也可以通过特征提取来降低标注字典的维数，从而降低学习任务的计算复杂度。我们的算法应用于高光谱成像和心电图数据分类的计算实例也被提出。
Dictionary learning, aiming at representing a signal in terms of the atoms of a dictionary, has gained popularity in a wide range of applications, including, but not limited to, image denoising, face recognition, remote sensing, medical imaging and feature extraction. Dictionary learning can be seen as a possible data-driven alternative to solve inverse problems by identifying the data with possible outputs that are either generated numerically using a forward model or the results of earlier observations of controlled experiments. Sparse dictionary learning is particularly interesting when the underlying signal is known to be representable in terms of a few vectors in a given basis. In this paper, we propose to use hierarchical Bayesian models for sparse dictionary learning that can capture features of the underlying signals, e.g. sparse representation and nonnegativity. The same framework can be employed to reduce the dimensionality of an annotated dictionary through feature extraction, thus reducing the computational complexity of the learning task. Computed examples where our algorithms are applied to hyperspectral imaging and classification of electrocardiogram data are also presented.