arXiv subjects

Fakhriyya Mammadova

Publications and source records attributed to Fakhriyya Mammadova.

2 recordsLinked to original sources

arXiv2025

Structured Random Models for Phase Retrieval with Optical Diffusers

Phase retrieval is a nonlinear inverse problem that arises in a wide range of imaging modalities, from electron microscopy to Fourier ptychography. In particular, the reconstruction is facilitated when the sensing matrix is i.i.d. random, enabling strong theoretical guarantees and efficient reconstruction algorithms. However, its applicability is restricted by excessive computational costs. In this paper, we propose structured random models for phase retrieval, where we emulate a dense random matrix by a cascade of structured transforms and random diagonal matrices. We reduce the complexity from quadratic to log-linear at no cost in reconstruction performance. Through a spectral method initialization followed by gradient descent, robust reconstruction is obtained at an oversampling ratio as low as 2.8. Moreover, we observe that the reconstruction performance is solely determined by the singular-value distribution of the forward matrix. This class of models can directly be implemented with basic optical elements such as lenses and diffusers, paving the way for large-scale phase imaging with robust reconstruction guarantees.

physics.optics↗

arXiv2025

Physics-Aware Style Transfer for Adaptive Holographic Reconstruction

Inline holographic imaging presents an ill-posed inverse problem of reconstructing objects' complex amplitude from recorded diffraction patterns. Although recent deep learning approaches have shown promise over classical phase retrieval algorithms, they often require high-quality ground truth datasets of complex amplitude maps to achieve a statistical inverse mapping operation between the two domains. Here, we present a physics-aware style transfer approach that interprets the object-to-sensor distance as an implicit style within diffraction patterns. Using the style domain as the intermediate domain to construct cyclic image translation, we show that the inverse mapping operation can be learned in an adaptive manner only with datasets composed of intensity measurements. We further demonstrate its biomedical applicability by reconstructing the morphology of dynamically flowing red blood cells, highlighting its potential for real-time, label-free imaging. As a framework that leverages physical cues inherently embedded in measurements, the presented method offers a practical learning strategy for imaging applications where ground truth is difficult or impossible to obtain.

physics.optics↗