论文标题
在耐力空间中的阶段检索
Phase Retrieval in Hardy Space
论文作者
论文摘要
本文涉及从强度测量$ | f（z）|，\ z \ in \ D中重建功能$ f $在\ D中的功能$ f $的研究。我们将其转换为通过Nevanlinna分解定理求解相应的外部和内部函数。外部函数将基于机械正交方法建立，而我们使用两种不同的方法来找出Blashcke乘积的零点，从而在假设奇异内部函数部分是微不足道的假设下计算内部函数。然后是混凝土算法和说明性实验。最后，我们通过引入放松的自适应傅立叶分解来稀疏表示$ f $。
This paper concerns the study of reconstructing a function $f$ in the Hardy space of the unit disc $\D$ from intensity measurements $|f(z)|,\ z\in \D.$ It's known as the problem of phase retrieval. We transform it into solving the corresponding outer and inner function through the Nevanlinna factorization Theorem. The outer function will be established based on the mechanical quadrature method, while we use two different ways to find out the zero points of Blashcke product, thereby computing the inner function under the assumption that the singular inner function part is trivial. Then the concrete algorithms and illustrative experiments follow. Finally, we give a sparse representation of $f$ by introducing the unwinding adaptive Fourier decomposition.
