Learning phase diversity for solving ill-posed inverse problems in imaging

TL;DR

This work tackles the fundamental ill-posedness of imaging inverse problems by introducing physics-informed pseudo-data generation: a neural network learns the implicit relationship between a single-shot measurement $y_1$ and a phase-diverse second measurement $y_2$, enabling a synthetic second shot $y'_2$ without extra hardware. The method is instantiated for both incoherent and coherent imaging using vortex-phase diversity, with a UNet trained to map $y_1$ to $y'_2$ and integrated with established reconstruction approaches such as Generalized Wiener filtering and spiral-phase phase retrieval. Quantitative results show that $y'_2$ closely approximates true $y_2$ (SSIM near 0.98) and that reconstructions using $(y_1,y'_2)$ rival those using $(y_1,y_2)$, while the cascaded GW filter delivers superior high-frequency content and contrast. The proposed framework promises hardware-light, high-fidelity computational imaging across modalities by reducing ill-posedness through learned data diversity and simple, robust reconstruction pipelines.

Abstract

Inverse problems in imaging are typically ill-posed and are usually solved by employing regularized optimization techniques. The usage of appropriate constraints can restrict the solution space, thus making it feasible for a reconstruction algorithm to find a meaningful solution. In recent years, deep network based ideas aimed at learning the end-to-end mapping between the raw measurements and the target image have gained popularity. In the learning approach, the functional relationship between the measured raw data and the solution image are learned by training a deep network with prior examples. While this approach allows one to significantly increase the real-time operational speed, it does not change the nature of the underlying ill-posed inverse problem. It is well-known that availability of diverse non-redundant data via additional measurements can generically improve the robustness of the reconstruction algorithms. The multiple data measurements, however, typically demand additional hardware and complex system setups that are not desirable. In this work, we note that in both incoherent and coherent optical imaging, the irradiance patterns corresponding to two phase diverse measurements associated with the same test object have implicit local correlation which may be learned. A physics informed data augmentation scheme is then described where a trained network is used for generating a phase diverse pseudo-data based on a ground truth data frame. The true data along with the augmented pesudo-data are observed to provide high quality inverse solutions with simpler reconstruction algorithms. We validate this approach for both incoherent and coherent optical imaging (or phase retrieval) configurations with vortex phase as a diversity mechanism. Our results may open new avenues for leaner high-fidelity computational imaging systems across a broad range of applications.

Figures (9)

• Figure 1: Imaging workflow. (a) Conventional multi-shot method acquires multiple datasets with varied illuminations/optical components for computational image reconstruction of the target object; (b) proposed method generates second-shot data using deep learning, bypassing additional hardware modifications; (c) computational processing techniques to solve imaging inverse problem.
• Figure 2: OTF magnitude for (a) open circular aperture and (b) spiral phase aperture, (c) profile plots of the two OTF magnitudes along the dotted central line in (a) and (b).
• Figure 3: Single shot vs. multi-shot imaging workflow for (a) incoherent and (b) coherent regimes. For multi-shot imaging, two image data were acquired without and with a charge-1 vortex phase plate placed in Fourier plane aperture for incoherent imaging and in illumination plane for coherent imaging.
• Figure 4: Computational techniques used to reconstruct images from the multi-shot data for (a) incoherent imaging and (b) coherent imaging case. FT stands for Fourier transform, IFT for inverse Fourier transform.
• Figure 5: UNet based deep learning architecture used to generate pseudo-data for both coherent and incoherent imaging.