离散层析成像问题解的差异性研究II
On the difference between solutions of discrete tomography problems II
摘要：
我们考虑的问题，重建二进制图像的水平和垂直投影。已知投影不一定唯一地确定图像。在以前的论文中，它表明，两个解决方案（二进制图像，满足投影）之间的对称差是最多4A倍的平方根的2N。这里，N是一个方向上的投影的总和（即图像的大小），A是取决于投影的参数。本文给出了一个下界：对于至少有两个解的投影集，我们构造两个对称差至少为2 A +2的解。我们还表明，这是最好的可能。
英文摘要：
We consider the problem of reconstructing binary images from their horizontal and vertical projections. It is known that the projections do not necessarily determine the image uniquely. In a previous paper it was shown that the symmetric difference between two solutions (binary images that satisfy the projections) is at most 4A times the square root of 2N. Here N is the sum of the projections in one direction (i.e. the size of the image) and A is a parameter depending on the projections. In this paper we give a lower bound: for each set of projections that has at least two solutions, we construct two solutions that have a symmetric difference of at least 2A+2. We also show that this is the best possible.
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。
