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.

翻译：在本文中,我们展示了如何直接通过相当于作为外产产品而获得的“升降信号”的矩形草图(ROP)来进行信号估计,而没有明确重建该信号。我们的分析依据的是,在微小的贬低伎俩下,ROP测量操作员满足了一个通用的信号产品嵌入(SPE)属性。在一段简略的外壳中,SPE显示,一个带有特定模式草图“信号”的信号草图的星标产品与该模式上该信号的投影方形相近。这相当于在ROP草图中插入一个ROP模型(“感知”)。我们的方法的有效性在一些合成实验中得到了评估。