Dictionaries for Sparse Representation Modeling
Dictionaries for Sparse Representation Modeling
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DOI：
10.1109/jproc.2010.2040551
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发表时间：
2010-06-01
影响因子：
20.6
通讯作者：
Elad, Michael
中科院分区：
文献类型：
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作者：
Rubinstein, Ron;Bruckstein, Alfred M.;Elad, Michael
数据的稀疏和冗余表示建模假设能够将信号描述为来自预先指定的字典的几个原子的线性组合。因此，稀疏化信号的字典的选择对于该模型的成功至关重要。一般来说，可以使用两种方式之一来选择合适的字典：i）基于数据的数学模型构建稀疏化字典，或者ii）学习字典以在训练集上表现最佳。在本文中，我们描述了这两种范式的演变。作为第一种方法的表现形式，我们涵盖的主题，如小波，小波包，contourlets和curvelets，所有的目的是利用1-D和2-D的数学模型，为信号和图像构建有效的字典。词典学习则采取了另一种方式，将词典与它应该服务的一组示例联系起来。从Field和Olshausen的开创性工作，通过MOD，K-SVD，广义PCA等，本文调查了各种选择，这样的培训，提供了最新的贡献和结构。
Sparse and redundant representation modeling of data assumes an ability to describe signals as linear combinations of a few atoms from a pre-specified dictionary. As such, the choice of the dictionary that sparsifies the signals is crucial for the success of this model. In general, the choice of a proper dictionary can be done using one of two ways: i) building a sparsifying dictionary based on a mathematical model of the data, or ii) learning a dictionary to perform best on a training set. In this paper we describe the evolution of these two paradigms. As manifestations of the first approach, we cover topics such as wavelets, wavelet packets, contourlets, and curvelets, all aiming to exploit 1-D and 2-Dmathematical models for constructing effective dictionaries for signals and images. Dictionary learning takes a different route, attaching the dictionary to a set of examples it is supposed to serve. From the seminal work of Field and Olshausen, through the MOD, the K-SVD, the Generalized PCA and others, this paper surveys the various options such training has to offer, up to the most recent contributions and structures.