论文标题
ROP成立：二次随机素描的信号估计
ROP inception: signal estimation with quadratic random sketching
论文作者
论文摘要
信号的矩阵和二次随机素描的排名一项投影（ROP）支持多种数据处理和机器学习方法，以及最新的成像应用程序，例如相位检索或光学处理单元。在本文中，我们演示了如何通过此类二次草图直接操作信号估计，这与无明确重建该信号的“抬高信号”的ROP相等。我们的分析依赖于表明，在较小的伪造技巧中，ROP测量操作员满足了广义标志产品嵌入（SPE）属性。简而言之，SPE表明，信号草图的标量乘积带有给定模式的草图的“符号”近似于该模式上该信号的投影的平方。因此，这相当于ROP草图中的ROP模型的插入（一个“成立”）。在几个合成实验中评估了我们方法的有效性。
Rank-one projections (ROP) of matrices and quadratic random sketching of signals support several data processing and machine learning methods, as well as recent imaging applications, such as phase retrieval or optical processing units. In this paper, we demonstrate how signal estimation can be operated directly through such quadratic sketches--equivalent to the ROPs of the "lifted signal" obtained as its outer product with itself--without explicitly reconstructing that signal. Our analysis relies on showing that, up to a minor debiasing trick, the ROP measurement operator satisfies a generalised sign product embedding (SPE) property. In a nutshell, the SPE shows that the scalar product of a signal sketch with the "sign" of the sketch of a given pattern approximates the square of the projection of that signal on this pattern. This thus amounts to an insertion (an "inception") of a ROP model inside a ROP sketch. The effectiveness of our approach is evaluated in several synthetic experiments.
