论文标题
阶段检索的局部性和稳定性
Locality and stability for phase retrieval
论文作者
论文摘要
trage $（x_j）_ {j \ in J} $ for a Hilbert space $ h $据说可以进行阶段检索，如果对于所有不同的矢量$ x，y \ in h $ in h h $ a框架系数的幅度$（| \ langle x，x_jj \ rangle |） x_j \ rangle |）_ {j \ in J} $区分$ x $与$ y $（最多达到单模型的标量）。我们考虑较弱的条件，其中框架系数的大小将$ x $与$ x $的小社区（最高为单模型标量）区分开。我们证明，对于某些定理完全不同的局部条件，一些相位检索的重要定理。我们也证明，在考虑阶段检索的稳定性时，在正交矢量中总是见证了最严重的稳定性不平等。考虑到相位检索的优化问题时，可以进行更简单的计算。
A frame $(x_j)_{j\in J}$ for a Hilbert space $H$ is said to do phase retrieval if for all distinct vectors $x,y\in H$ the magnitude of the frame coefficients $(|\langle x, x_j\rangle|)_{j\in J}$ and $(|\langle y, x_j\rangle|)_{j\in J}$ distinguish $x$ from $y$ (up to a unimodular scalar). We consider the weaker condition where the magnitude of the frame coefficients distinguishes $x$ from every vector $y$ in a small neighborhood of $x$ (up to a unimodular scalar). We prove that some of the important theorems for phase retrieval hold for this local condition, where as some theorems are completely different. We prove as well that when considering stability of phase retrieval, the worst stability inequality is always witnessed at orthogonal vectors. This allows for much simpler calculations when considering optimization problems for phase retrieval.
