论文标题
从晶格测量中检索Gabor相的注入性
Injectivity of Gabor phase retrieval from lattice measurements
论文作者
论文摘要
我们为Gabor阶段检索问题建立了新颖的唯一性结果：如果$ \ Mathcal {g}：l^2（\ Mathbb {r}）\ to l^2（\ Mathbb {r}^2）$表示Gabor转换，则每个$ f \ in l^4 [ - \ tfrac {c} {2}，\ tfrac {c} {2}] $由值$ | \ nathcal {g} f（x，ω）| $（x，x，x，ω）$确定为全局阶段。 （2C）^{ - 1} \ Mathbb {z} $和$ b> 0 $是任意的正常数。这首先表明，紧凑型，复杂值的功能可以独特地从其光谱图的晶格样品中重建。此外，通过利用Gröchenig，Romero和Stöckler在Shiftistranvaniant空间中采样相关的最新发展，我们证明了与高斯发电机的换档不变空间的功能相似的唯一性结果。还提出了对非均匀抽样的概括。最后，我们将结果与假定为实现的信号进行了比较。
We establish novel uniqueness results for the Gabor phase retrieval problem: if $\mathcal{G} : L^2(\mathbb{R}) \to L^2(\mathbb{R}^2)$ denotes the Gabor transform then every $f \in L^4[-\tfrac{c}{2},\tfrac{c}{2}]$ is determined up to a global phase by the values $|\mathcal{G}f(x,ω)|$ where $(x,ω)$ are points on the lattice $b^{-1}\mathbb{Z} \times (2c)^{-1}\mathbb{Z}$ and $b>0$ is an arbitrary positive constant. This for the first time shows that compactly-supported, complex-valued functions can be uniquely reconstructed from lattice samples of their spectrogram. Moreover, by making use of recent developments related to sampling in shift-invariant spaces by Gröchenig, Romero and Stöckler, we prove analogous uniqueness results for functions in shift-invariant spaces with Gaussian generator. Generalizations to nonuniform sampling are also presented. Finally, we compare our results to the situation where the considered signals are assumed to be real-valued.
