Phase retrieval refers to the problem of recovering some signal (which is often modelled as an element of a Hilbert space) from phaseless measurements. It has been shown that in the deterministic setting phase retrieval from frame coefficients is always unstable in infinite-dimensional Hilbert spaces (Cahill et al. in Trans Am Math Soc Ser B 3(3):63–76, 2016) and possibly severely ill-conditioned in finite-dimensional Hilbert spaces (Cahill et al. in Trans Am Math Soc Ser B 3(3):63–76, 2016). Recently, it has also been shown that phase retrieval from measurements induced by the Gabor transform with Gaussian window function is stable under a more relaxed semi-global phase recovery regime based on atoll functions (Alaifari in Found Comput Math 19(4):869–900, 2019). In finite dimensions, we present first evidence that this semi-global reconstruction regime allows one to do phase retrieval from measurements of bandlimited signals induced by the discrete Gabor transform in such a way that the corresponding stability constant only scales like a low order polynomial in the space dimension. To this end, we utilise reconstruction formulae which have become common tools in recent years (Bojarovska and Flinth in J Fourier Anal Appl 22(3):542–567, 2016; Eldar et al. in IEEE Signal Process Lett 22(5):638–642, 2014; Li et al. in IEEE Signal Process Lett 24(4):372–376, 2017; Nawab et al. in IEEE Trans Acoust Speech Signal Process 31(4):986–998, 1983).

相位检索是指从无相测量中恢复某些信号（通常将其建模为希尔伯特空间的一个元素）的问题。结果表明，在确定性设置中，在无限维希尔伯特空间中，从帧系数中进行相位检索总是不稳定的（Cahill等人在Trans Am Math Soc Ser B 3（3）：63-76，2016中），可能病情严重有限维希尔伯特空间中的条件（Cahill等人，Trans Am Math Soc Ser B 3（3）：63–76，2016）。最近，研究还表明，在基于环礁函数的更为宽松的半全局相位恢复机制下，从具有高斯窗函数的Gabor变换所引起的测量中获取相位是稳定的（Alaifari在Found Comput Math 19（4）：869–900，2019中）。在有限维度中，我们提供了第一个证据，即这种半全局重建机制允许人们从由离散Gabor变换引起的带限信号的测量中进行相位检索，使得相应的稳定性常数仅像低阶多项式那样缩放。空间尺寸。为此，我们利用了近年来成为常用工具的重构公式（Bojarovska和Flinth在J Fourier Anal Appl 22（3）：542-567，2016; Eldar等人在IEEE Signal Process Lett 22（5）中： 638–642，2014； Li等人在IEEE Signal Process Lett 24（4）：372–376，2017; Nawab等人在IEEE Trans Acoust语音信号处理31（4）：986–998，1983）。