We study the recovery of functions in real spline spaces from unsigned sampled values. We consider two types of recovery. The one is to recover functions locally from finitely many unsigned samples. And the other is to recover functions on the whole line from infinitely many unsigned samples. In both cases, we give characterizations for a sequence of distinct points to be a phaseless sampling sequence, at which any nonseparable function is determined up to a sign on an interval or on the whole line by its unsigned sampled values. Moreover, for the case of local recovery, we also study the almost phaseless sampling and give a necessary and sufficient condition for a sequence of points to admit local recovery for almost all functions.

中文翻译：

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真实样条空间中的局部和全局无相采样

我们研究了从无符号采样值中恢复真实样条空间中的函数。我们考虑两种类型的恢复。一种是从有限多个无符号样本中本地恢复函数。另一种是从无限多的无符号样本中恢复整条线的函数。在这两种情况下，我们都将一系列不同点的特征描述为无相采样序列，在该序列中，任何不可分离的函数都由其无符号采样值确定到一个区间或整条线上的符号。此外，对于局部恢复的情况，我们还研究了几乎无相采样，并给出了一系列点允许几乎所有函数的局部恢复的充要条件。