论文标题
扩张的POC：Minimax凸优化
Dilated POCS: Minimax Convex Optimization
论文作者
论文摘要
交替投影到凸集（POC）提供了一个迭代过程，可以找到一个满足两个或多个凸约限制时的信号。对于非电向约束，同时投影的方法会产生最小平方误差（MMSE）解决方案。在某些情况下，最小化解决方案更可取。使用扩张的POC可以生成最小溶液。 Minimax溶液使用非电向信号凸约束的形态扩张。将集合逐渐扩张到最小溶液处的相交点。给出了示例与图像层析结构问题中的MMSE和Minimax解决方案进行对比。扩张的POC为图像合成添加了一种新的成像方式。最后，建议信号集的形态侵蚀是一种方法，即在一个以上的一个点以上相交时缩小重叠的方法。
Alternating projection onto convex sets (POCS) provides an iterative procedure to find a signal that satisfies two or more convex constraints when the sets intersect. For nonintersecting constraints, the method of simultaneous projections produces a minimum mean square error (MMSE) solution. In certain cases, a minimax solution is more desirable. Generating a minimax solution is possible using dilated POCS. The minimax solution uses morphological dilation of nonintersecting signal convex constraints. The sets are progressively dilated to the point where there is intersection at a minimax solution. Examples are given contrasting the MMSE and minimax solutions in problems of tomographic reconstruction of images. Dilated POCS adds a new imaging modality for image synthesis. Lastly, morphological erosion of signal sets is suggested as a method to shrink the overlap when sets intersect at more than one point.
