Separable cosparse Analysis Operator learning
Separable cosparse Analysis Operator learning
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发表时间：
2014-06
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通讯作者：
Matthias Seibert;Julian Wörmann;R. Gribonval;M. Kleinsteuber
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作者：
Matthias Seibert;Julian Wörmann;R. Gribonval;M. Kleinsteuber
具有针对某类信号的稀疏表示的能力在数据分析、图像处理和其他研究领域中具有许多应用。在稀疏表示中，cosparse分析模型最近得到了越来越多的关注。许多信号表现出多维结构，例如图像或三维MRI扫描。大多数数据分析和学习算法使用矢量化信号，因此不考虑这种底层结构。不考虑固有结构的缺点是计算成本急剧增加。我们提出了一个算法，学习cosparse分析运算符，坚持预先存在的数据结构，从而允许一个非常有效的实现。这是通过在学习的算子上强制可分离的结构来实现的。我们的学习算法能够处理任意阶的多维数据。我们评估我们的方法在三维MRI扫描的例子体积数据。
The ability of having a sparse representation for a certain class of signals has many applications in data analysis, image processing, and other research fields. Among sparse representations, the cosparse analysis model has recently gained increasing interest. Many signals exhibit a multidimensional structure, e.g. images or three-dimensional MRI scans. Most data analysis and learning algorithms use vectorized signals and thereby do not account for this underlying structure. The drawback of not taking the inherent structure into account is a dramatic increase in computational cost. We propose an algorithm for learning a cosparse Analysis Operator that adheres to the preexisting structure of the data, and thus allows for a very efficient implementation. This is achieved by enforcing a separable structure on the learned operator. Our learning algorithm is able to deal with multidimensional data of arbitrary order. We evaluate our method on volumetric data at the example of three-dimensional MRI scans.