论文标题
基质从双线性和二次测量中恢复
Matrix recovery from bilinear and quadratic measurements
论文作者
论文摘要
矩阵（或操作员）从线性测量中恢复是一个充分研究的问题。但是，在某些情况下，只有双线性或二次测量。双线性或二次问题可以很容易地转化为线性问题，但是当线性化问题是可以解决的，而线性化的成本是多少，它会提出问题。在这项工作中，我们研究了这个总体问题的一些具体情况，并显示了何时可以解决双线性问题。使用此结果和多项式环的某些属性，我们提出了一个方案，当二次问题可以以仅线性数量的其他测量成本为本性化时。最后，我们将结果链接回两个启发它的应用程序：时间编码机器和连续本地化。
Matrix (or operator) recovery from linear measurements is a well-studied problem. However, there are situations where only bilinear or quadratic measurements are available. A bilinear or quadratic problem can easily be transformed into a linear one, but it raises questions when the linearized problem is solvable and what is the cost of linearization. In this work, we study a few specific cases of this general problem and show when the bilinear problem is solvable. Using this result and certain properties of polynomial rings, we present a scenario when the quadratic problem can be linearized at the cost of just a linear number of additional measurements. Finally, we link our results back to two applications that inspired it: Time Encoding Machines and Continuous Localisation.
