论文标题
崩溃总和的逆问题
An inverse problem for the collapsing sum
论文作者
论文摘要
高斯过滤器在计算机科学的各个领域都有应用，从计算机视觉到语音识别。崩溃的总和是一个矩阵运算符，最近引入了用于研究高斯过滤器的组合。在本文中，我们从离散的层析角度将崩溃的总和视为矩阵完成问题的可恢复性。使用两分图，我们得出了将部分矩阵扩展到给定矩阵的预先映射的必要条件。
Gaussian filters have applications in a variety of areas in computer science, from computer vision to speech recognition. The collapsing sum is a matrix operator that was recently introduced to study Gaussian filters combinatorially. In this paper, we view the collapsing sum from a discrete tomographical perspective and examine the recoverability of its preimages as a matrix completion problem. Using bipartite graphs, we derive a necessary and sufficient condition for a partial matrix to be extended to a preimage of a given matrix.
