具有可分离结构的协稀疏分析算子的学习
Learning Co-Sparse Analysis Operators with Separable Structures
摘要：
在共稀疏分析模型中，将一组滤波器应用于感兴趣的信号类别之外的信号，从而产生稀疏滤波器响应。因此，它可以作为逆问题的先验，或用于已知属于信号类的信号的结构分析。模型越适合于类，它就越可靠。因此，学习给定类的此类运算符的任务是一个至关重要的问题。在许多应用中，还要求以及时的方式获得滤波器响应，这可以通过具有可分离结构的滤波器来实现。这类算子不仅可以有效地用于计算滤波器响应，而且它们还具有需要较少的训练样本来获得算子的可靠估计的优点。这项工作的第一个贡献是通过提供学习过程的样本复杂性的上限来为这一主张提供理论证据。第二种是随机梯度下降（SGD）方法，旨在学习一个分析算子与可分离的结构，其中包括一个新的和有效的步长选择规则。数值实验提供链接的样本复杂性的SGD算法的收敛速度。
英文摘要：
In the co-sparse analysis model a set of filters is applied to a signal out of the signal class of interest yielding sparse filter responses. As such, it may serve as a prior in inverse problems, or for structural analysis of signals that are known to belong to the signal class. The more the model is adapted to the class, the more reliable it is for these purposes. The task of learning such operators for a given class is therefore a crucial problem. In many applications, it is also required that the filter responses are obtained in a timely manner, which can be achieved by filters with a separable structure. Not only can operators of this sort be efficiently used for computing the filter responses, but they also have the advantage that less training samples are required to obtain a reliable estimate of the operator. The first contribution of this work is to give theoretical evidence for this claim by providing an upper bound for the sample complexity of the learning process. The second is a stochastic gradient descent (SGD) method designed to learn an analysis operator with separable structures, which includes a novel and efficient step size selection rule. Numerical experiments are provided that link the sample complexity to the convergence speed of the SGD algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
