DOLPHIn -用于相位恢复的字典学习
DOLPHIn - Dictionary Learning for Phase Retrieval
摘要：
我们提出了一种新的算法来学习字典重建和稀疏编码信号的测量没有相位。具体而言，我们认为，估计一个二维图像的任务，从平方幅度测量的复值线性变换的原始图像。几个最近的相位恢复算法利用潜在的稀疏性的未知信号，以提高恢复性能。在这项工作中，我们认为这样一个稀疏的信号相位恢复的背景下，事先不知道的稀疏字典。我们的算法联合重建未知信号-可能被噪声破坏-并学习字典，使得估计图像的每个补丁可以稀疏表示。数值实验表明，我们的方法可以获得显着更好的重建相位恢复问题的噪声比方法，不能利用这种“隐藏”稀疏。此外，在理论方面，我们提供了我们的方法的收敛结果。
英文摘要：
We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements of a complex-valued linear transformation of the original image. Several recent phase retrieval algorithms exploit underlying sparsity of the unknown signal in order to improve recovery performance. In this work, we consider such a sparse signal prior in the context of phase retrieval, when the sparsifying dictionary is not known in advance. Our algorithm jointly reconstructs the unknown signal - possibly corrupted by noise - and learns a dictionary such that each patch of the estimated image can be sparsely represented. Numerical experiments demonstrate that our approach can obtain significantly better reconstructions for phase retrieval problems with noise than methods that cannot exploit such "hidden" sparsity. Moreover, on the theoretical side, we provide a convergence result for our method.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
