论文标题
新型的最低最大逆向反向问题的重新纠正
Novel min-max reformulations of Linear Inverse Problems
论文作者
论文摘要
在本文中，我们介入了所谓的不正确的线性反问题（LIP）的类别，这些线性反向问题（LIP）只是指从相对较少的随机线性测量结果中恢复整个信号的任务。此类问题在各种环境中出现，其应用程序从医学图像处理，推荐系统等。我们提出了错误约束线性逆问题的稍微概括的版本，并通过提供对其凸几何形状的曝光来获得新颖且同等的凸线conconcove Min-Max重新印象。最低 - 最大问题的鞍点是完全以对唇部解决方案的方式来表征的，反之亦然。应用简单的鞍点寻求上升呈淡入型算法来解决最小值问题，提供了新颖而简单的算法，以找到唇部的解决方案。此外，作为本文中提供的最低 - 最大问题的嘴唇的重新制作对于开发方法以几乎确定的恢复限制来解决词典学习问题至关重要。
In this article, we dwell into the class of so-called ill-posed Linear Inverse Problems (LIP) which simply refers to the task of recovering the entire signal from its relatively few random linear measurements. Such problems arise in a variety of settings with applications ranging from medical image processing, recommender systems, etc. We propose a slightly generalized version of the error constrained linear inverse problem and obtain a novel and equivalent convex-concave min-max reformulation by providing an exposition to its convex geometry. Saddle points of the min-max problem are completely characterized in terms of a solution to the LIP, and vice versa. Applying simple saddle point seeking ascend-descent type algorithms to solve the min-max problems provides novel and simple algorithms to find a solution to the LIP. Moreover, the reformulation of an LIP as the min-max problem provided in this article is crucial in developing methods to solve the dictionary learning problem with almost sure recovery constraints.
