论文标题
基于近端梯度方法应用于卷积稀疏问题的有效共识模型
Efficient Consensus Model based on Proximal Gradient Method applied to Convolutional Sparse Problems
论文作者
论文摘要
卷积稀疏表示（CSR）是反问题的转移不变模型，在信号/图像处理，机器学习和计算机视觉的领域引起了很多关注。 CSR中最具挑战性的问题意味着形式的$ min_x \ sum_i f_i（x） + g（x）$的复合函数的最小化，在这种情况下，直接和低成本解决方案很难实现。但是，据报道，半分布的配方（例如ADMM共识）可以提供重要的计算效益。在目前的工作中，我们得出并详细介绍了基于近端梯度（PG）方法的有效共识算法的彻底理论分析。在经典的卷积词典学习问题中，主要评估了所提出的算法相对于其ADMM对应物的有效性。此外，我们的共识方法（通常是结构化的）可以用于解决其他优化问题，其中凸函数的总和具有正则化项共享一个单个全局变量。例如，在异常检测任务中，提出的算法也应用于另一个特定的卷积问题。
Convolutional sparse representation (CSR), shift-invariant model for inverse problems, has gained much attention in the fields of signal/image processing, machine learning and computer vision. The most challenging problems in CSR implies the minimization of a composite function of the form $min_x \sum_i f_i(x) + g(x)$, where a direct and low-cost solution can be difficult to achieve. However, it has been reported that semi-distributed formulations such as ADMM consensus can provide important computational benefits. In the present work, we derive and detail a thorough theoretical analysis of an efficient consensus algorithm based on proximal gradient (PG) approach. The effectiveness of the proposed algorithm with respect to its ADMM counterpart is primarily assessed in the classic convolutional dictionary learning problem. Furthermore, our consensus method, which is generically structured, can be used to solve other optimization problems, where a sum of convex functions with a regularization term share a single global variable. As an example, the proposed algorithm is also applied to another particular convolutional problem for the anomaly detection task.
