Since their inception in the 1930–1960s, the research disciplines of computational imaging and machine learning have followed parallel tracks and, during the last two decades, experienced explosive growth drawing on similar progress in mathematical optimization and computing hardware. While these developments have always been to the benefit of image interpretation and machine vision, only recently has it become evident that machine learning architectures, and deep neural networks in particular, can be effective for computational image formation, aside from interpretation. The deep learning approach has proven to be especially attractive when the measurement is noisy and the measurement operator ill posed or uncertain. Examples reviewed here are: super-resolution; lensless retrieval of phase and complex amplitude from intensity; photon-limited scenes, including ghost imaging; and imaging through scatter. In this paper, we cast these works in a common framework. We relate the deep-learning-inspired solutions to the original computational imaging formulation and use the relationship to derive design insights, principles, and caveats of more general applicability. We also explore how the machine learning process is aided by the physics of imaging when ill posedness and uncertainties become particularly severe. It is hoped that the present unifying exposition will stimulate further progress in this promising field of research.

Most of the neural networks proposed so far for computational imaging (CI) in optics employ a supervised training strategy, and thus need a large training set to optimize their weights and biases. Setting aside the requirements of environmental and system stability during many hours of data acquisition, in many practical applications, it is unlikely to be possible to obtain sufficient numbers of ground-truth images for training. Here, we propose to overcome this limitation by incorporating into a conventional deep neural network a complete physical model that represents the process of image formation. The most significant advantage of the resulting physics-enhanced deep neural network (PhysenNet) is that it can be used without training beforehand, thus eliminating the need for tens of thousands of labeled data. We take single-beam phase imaging as an example for demonstration. We experimentally show that one needs only to feed PhysenNet a single diffraction pattern of a phase object, and it can automatically optimize the network and eventually produce the object phase through the interplay between the neural network and the physical model. This opens up a new paradigm of neural network design, in which the concept of incorporating a physical model into a neural network can be generalized to solve many other CI problems.

Ghost imaging (GI) facilitates image acquisition under low-light conditions by single-pixel measurements and thus has great potential in applications in various fields ranging from biomedical imaging to remote sensing. However, GI usually requires a large amount of single-pixel samplings in order to reconstruct a high-resolution image, imposing a practical limit for its applications. Here we propose a far-field super-resolution GI technique that incorporates the physical model for GI image formation into a deep neural network. The resulting hybrid neural network does not need to pre-train on any dataset, and allows the reconstruction of a far-field image with the resolution beyond the diffraction limit. Furthermore, the physical model imposes a constraint to the network output, making it effectively interpretable. We experimentally demonstrate the proposed GI technique by imaging a flying drone, and show that it outperforms some other widespread GI techniques in terms of both spatial resolution and sampling ratio. We believe that this study provides a new framework for GI, and paves a way for its practical applications.

In this manuscript, we propose a novel framework of computational ghost imaging, i.e., ghost imaging using deep learning (GIDL). With a set of images reconstructed using traditional GI and the corresponding ground-truth counterparts, a deep neural network was trained so that it can learn the sensing model and increase the quality image reconstruction. Moreover, detailed comparisons between the image reconstructed using deep learning and compressive sensing shows that the proposed GIDL has a much better performance in extremely low sampling rate. Numerical simulations and optical experiments were carried out for the demonstration of the proposed GIDL.

Artificial intelligence (AI) techniques such as deep learning (DL) for computational imaging usually require to experimentally collect a large set of labeled data to train a neural network. Here we demonstrate that a practically usable neural network for computational imaging can be trained by using simulation data. We take computational ghost imaging (CGI) as an example to demonstrate this method. We develop a one-step end-to-end neural network, trained with simulation data, to reconstruct two-dimensional images directly from experimentally acquired one-dimensional bucket signals, without the need of the sequence of illumination patterns. This is in particular useful for image transmission through quasi-static scattering media as little care is needed to take to simulate the scattering process when generating the training data. We believe that the concept of training using simulation data can be used in various DL-based solvers for general computational imaging.

It is well known that in-line digital holography (DH) makes use of the full pixel count in forming the holographic imaging. But it usually requires phase-shifting or phase retrieval techniques to remove the zero-order and twin-image terms, resulting in the so-called two-step reconstruction process, i.e., phase recovery and focusing. Here, we propose a one-step end-to-end learning-based method for in-line holography reconstruction, namely, the eHoloNet, which can reconstruct the object wavefront directly from a single-shot in-line digital hologram. In addition, the proposed learning-based DH technique has strong robustness to the change of optical path difference between reference beam and object light and does not require the reference beam to be a plane or spherical wave.