Understanding Structured Random Models for Phase Retrieval
Zhiyuan Hu, Doctoral Student at EPFL
Structured random models have been proposed as an efficient alternative to fully random models for the phase retrieval problem, offering comparable reconstruction performance while reducing computational complexity from quadratic to log-linear. These models leverage a cascade of structured transforms and random diagonal matrices to enhance efficiency. In this work, we further generalize the definition of structured random models by using more types of structured transforms and diagonal matrices. Our studies reveal that the effectiveness of the forward model depends on the independence among the matrix components measured by covariance. Furthermore, the singular value distribution plays a key role in determining overall model performance. By configuring the magnitudes of the diagonal elements to control the spectral distribution, it is possible to achieve better reconstruction quality than an i.i.d. Gaussian model. This unlocks the possibility of achieving efficient optical implementations for random models in practice.
Zhiyuan Hu, Doctoral Student at EPFL
Meeting • 2025-04-15
AbstractStructured random models have been proposed as an efficient alternative to fully random models for the phase retrieval problem, offering comparable reconstruction performance while reducing computational complexity from quadratic to log-linear. These models leverage a cascade of structured transforms and random diagonal matrices to enhance efficiency. In this work, we further generalize the definition of structured random models by using more types of structured transforms and diagonal matrices. Our studies reveal that the effectiveness of the forward model depends on the independence among the matrix components measured by covariance. Furthermore, the singular value distribution plays a key role in determining overall model performance. By configuring the magnitudes of the diagonal elements to control the spectral distribution, it is possible to achieve better reconstruction quality than an i.i.d. Gaussian model. This unlocks the possibility of achieving efficient optical implementations for random models in practice.