Applied and Computational Harmonic Analysis ( IF 2.5 ) Pub Date : 2022-09-07 , DOI: 10.1016/j.acha.2022.09.001 Philipp Grohs, Lukas Liehr
We establish novel uniqueness results for the Gabor phase retrieval problem: if denotes the Gabor transform then every is determined up to a global phase by the values where are points on the lattice and 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.
中文翻译:
从晶格测量中检索 Gabor 相位的注入性
我们为 Gabor 相位检索问题建立了新的唯一性结果:如果表示 Gabor 变换,那么每个由值确定到全局阶段在哪里是格子上的点和是一个任意的正常数。这首次表明紧支持的复值函数可以从其频谱图的晶格样本中唯一地重建。此外,通过利用 Gröchenig、Romero 和 Stöckler 在移位不变空间中采样的最新进展,我们证明了具有高斯发生器的移位不变空间中的函数的类似唯一性结果。还介绍了对非均匀抽样的推广。最后,我们将我们的结果与假设所考虑的信号是实值的情况进行比较。