论文标题
棕榈：一种增强的近端交替线性化最小化算法，用于分离幅度和相位的正规化
PALMNUT: An Enhanced Proximal Alternating Linearized Minimization Algorithm with Application to Separate Regularization of Magnitude and Phase
论文作者
论文摘要
我们引入了一种新算法，用于复杂图像重建，并通过单独的图像幅度和相位进行正则化。在许多不同的图像重建上下文中，这种优化问题很有趣，尽管是非convex，并且很难解决。在这项工作中，我们首先描述了以前的近端交替线性化缩影（棕榈）算法的新颖实现，以解决此优化问题。然后，我们对棕榈进行增强，导致一种名为Palmnut的新算法，该算法将棕榈与Nesterov的动量结合在一起，并采用了一种新的方法，该方法依赖于从坐标为Lipschitz的coortionwise spep尺寸中取得的无偶联坐标台阶尺寸。从理论上讲，我们确定一种棕榈树（没有Nesterov的动量）单调降低目标函数，从而导致许多感兴趣的情况下会收敛。在磁共振成像的背景下获得的经验结果表明，棕榈树在诸如交替最小化之类的常见方法中具有计算优势。尽管我们的重点是分离大小和相正化的应用，但我们希望同样的方法在具有相似目标函数结构的其他非凸优化问题中也可能有用。
We introduce a new algorithm for complex image reconstruction with separate regularization of the image magnitude and phase. This optimization problem is interesting in many different image reconstruction contexts, although is nonconvex and can be difficult to solve. In this work, we first describe a novel implementation of the previous proximal alternating linearized minization (PALM) algorithm to solve this optimization problem. We then make enhancements to PALM, leading to a new algorithm named PALMNUT that combines the PALM together with Nesterov's momentum and a novel approach that relies on uncoupled coordinatewise step sizes derived from coordinatewise Lipschitz-like bounds. Theoretically, we establish that a version of PALMNUT (without Nesterov's momentum) monotonically decreases the objective function, leading to guaranteed convergence in many cases of interest. Empirical results obtained in the context of magnetic resonance imaging demonstrate that PALMNUT has computational advantages over common existing approaches like alternating minimization. Although our focus is on the application to separate magnitude and phase regularization, we expect that the same approach may also be useful in other nonconvex optimization problems with similar objective function structure.
